Edward was born in Marylebone, London, in May 1772 but there is, rather surprisingly, no record of his baptism. In May 1777, he went with his mother and his younger brother Samuel to join his father in Paris where the latter had gone to work for the American Commission there.

The Bancroft family stayed in Paris until June 1783 when they returned to live in London once more. Edward and his brother Samuel were sent to Dr William Rose's Academy at Chiswick. Following Dr Rose's death in July 1786, the Academy moved to Hammersmith and later to Greenwich under the headmastership of Dr Rose's son-in-law, Mr Charles Burney. It is said by some that Edward was also tutored by the Rev. Samuel Parr, a circumstance that would have required him to reside with the Rev. Parr at his Hatton Parsonage in Warwickshire if it was so, which seems unlikely.

During his time in Paris, Edward became very fluent in the French language judging by a surviving letter that he wrote to Dr Benjamin Franklin in November 1783, ⁵  that letter and others he wrote to Dr Franklin in 1784, show considerable maturity for someone aged 11½.

In the summer of 1789, Edward went up to St John's College Cambridge where he was admitted as a sizar (someone who is helped with college and university fees, etc., by way of a bursary/scholarship).^{6 7}  In 1793, he broke off from his studies to join Hon. Thomas Walpole as his private secretary when the latter was in Bavaria as Minister Plenipotentiary to the Elector Palatine ^{8 9} - this Thomas Walpole was the son of Edward's father's friend and sometime business colleague, Hon. Thomas Walpole, M.P. (1727-1803). Edward went back to St John's College as a "fellow commoner" in April 1794 and was awarded his MB at the end of that academic year. It is said that Edward then matriculated at Edinburgh University with a view to continuing his studies for his MD there but only completed one academic year before breaking off to seek practical experience in "the field".

Edward seems to have been drawn to the army hospital service very early in his career and he took up a post as Physician to the Forces between 1795 and 1802 and served with the Army in the Windward Islands, in Portugal, the Mediterranean, and in Egypt, latterly carrying much responsibility as a senior hospital doctor. If his father's Will of September 1802 is correct, Edward, then on half pay, went back to St John's College for a period,¹⁰ perhaps even a full academic year, before going back to the army on full pay in September 1803.¹¹ He did the so again in 1807 after another period on half pay. In 1804, he was awarded his MD from Cambridge; became a Member of the Royal College of Physicians in 1805, was elected a Fellow in 1806 and was honoured by being asked to give that year's Goulstonian Lecture to its members, which he did on the subject of Yellow Fever. During these years, it is said that he ran a private practice possibly based in Margaret Street, Cavendish Square, where he and his father had a house.

As mentioned earlier, he was briefly back on full pay from June 1807¹¹ but that appointment does not seem to have lasted very long as he joined the staff of St George's Hospital in 1808. He was also honoured by the Royal College that year by being appointed a Censor. A Censor was one of a select committee who oversaw the College's professional standards and Edward's appointment owed much, it is said, to his very public defence (by pamphleteering) of the authority of physicians over the growing assertiveness of army surgeons in military medical matters.

Once again, in July 1809,¹¹ he was summoned back to full time army employment but on this occasion, he declined due to ill-health and a copy has survived of part of a letter from him to The Right Honourable General Sir David Dundas, who was Commander-in-Chief at the time, explaining why he did not accompany the Earl of Chatham with the British Expeditionary Force to Holland^* that year.¹² Instead, he remained at St George's Hospital, finding time to write and publish an erudite essay^** expanding on his earlier lectures on Yellow Fever.

It is not clear why Edward switched back and forth between military and non-military medical practice during his years in London or later in Jamaica. Was it because the Army required his services (it was the time of the Napoleonic Wars) or because he requested to be put back on full pay because he was in need of income? Certainly, the latter appears to have been the case in 1840 (see later) but, generally, those put on service half pay, be they serving in the Army or the Navy, had to wait patiently hoping they would be given a new position.

In 1811, Edward was 39 years of age and, for some time, his health had been hampering his medical duties in England, both as an Army physician (see earlier) and at St George's Hospital. Clearly, a "change of air" was required and, presumably on the basis of his earlier experience of the West Indies, he decided that living there would improve his health and, as things turned out, it did, as he lived an active life in Jamaica for another 30 years avoiding the very Yellow Fever to which so many succumbed and on which he was an authority.

In the summer of that year, he resigned his post at St George's Hospital and sailed for Port Royal. Ironically, the newspaper report that confirms his presence there in October, refers to him as a "convalescent"!¹³ It is said by some that he took up a position as Physician to the Forces but there is no corroborating evidence, nevertheless, given his financial circumstances, that might have been the case. Alternatively, he may not have had an Army position to go to but chose Jamaica as the best place in the West Indies to set up in practice due to the Island's size and importance to the British at that time. Whatever the case may be, he did settle in Kingston and it is noteworthy that when he and Ursula Hoseason were married there in October 1812, there was no mention in their "marriage lines", or any newspaper report of their wedding, of him being employed as Physician to the Forces. ¹
  
In October 1815,¹¹ however, records do show that Edward was called back to full-time service as a Physician to the Forces on the Island and later elevated as to be brevet Deputy Inspector of Hospitals in July 1817, that the latter appointment ended in August 1818 when he went back on half pay, a state in which he was to remain for the next 20 years or so.

Edward's appointment to Deputy Inspector of Hospitals was probably announced when he and Ursula were in England with their first child, Ursula Maria, who had been given a Bancroft family christening at Margate earlier that year (she had already been baptised in Kingston). Later, in October that year, Ursula stayed on in England to have their second child, Edward James, while Edward, senior, sailed on his own for Jamaica, it was to be the last time he made that voyage as he never returned.^{14 15}
       
Surviving family papers and contemporary Jamaican newspapers give little indication of how Edward occupied himself following his return to half pay in 1818. Presumably, he continued to practice medicine either as a private physician or working in Kingston's public hospital, which he is reported to have done in 1839 & 1840,¹⁶ otherwise it seems unlikely that the Army would have taken him on again in 1840.¹¹ However, most reports concern meetings or dinners connected with the Horticultural Society of which he was president for many years¹⁷ or latterly in relation to the establishment of a Jamaican College of Physicians,¹⁸ a proposal that he, and others similarly qualified, supported against strong opposition from less well-qualified, local physicians. Edward's engagement in December 1840 as brevet Deputy Inspector General of Hospitals on the Island was the last of his public appointments and seems to have remained in place until his death aged 70, in September 1842. The appointment, it is said, was at Edward's request as he needed money to be able to send his son William to the Royal Military College at Sandhurst.

The 1820s and 30s brought Edward many family sadnesses. An infant son, George died in 1825 and in 1830 his beloved Ursula died "after much suffering" in childbirth in January 1830,^{19 20} followed shortly by the baby, Charles Augustus.²¹ Later, Edward was to lose both his elder children, Edward James dying in the late 1830s in Spain and Ursula Maria at home in 1840. Very fortunately, he lived long enough to see his daughter Augusta married to Peter Espeut — they were married by special licence at 2 am on September 18th 1842 at his bedside - and his surviving son William placed at Sandhurst as an officer cadet.
 
The Jamaican Royal Gazette published a lengthy obituary following Edward's death, said to be contributed by someone who knew him well. In summing up his career it said, "… a gentleman whose death we are persuaded will be greatly lamented by those who wished to be assisted in their laudable endeavours to obtain knowledge, for Doctor Bancroft was studiously attentive and patient, neither trouble, nor time, indisposition or occupation (unless of an extraordinary nature) were ever allowed to form obstacles either to his acquiring or imparting knowledge. He was in every sense a gentleman and a scholar, on whom nature had bestowed more than her ordinary gifts.".

A mural plaque commemorating his memory was placed by the physicians and surgeons of Jamaica in the Cathedral Church of Kingston as a token of the high regard in which he was held by them. The plaque reads: -

Edward Nathaniel Bancroft, M.D., Cantab, Fellow of the Royal College of Physicians, London, and Deputy Inspector General of Army Hospitals, (Erected by the Physicians and Surgeons of Jamaica). Ob. at Kingston 18th Sept., 1842, æt. 70.

Munk's Roll records the following quotation about Edward taken from Authentic Memoirs of the most Eminent Physicians and Surgeons of Great Britain (2nd edit. 8vo. Lond. 1818, p. 68.): "[Dr Bancroft's writings] 'display not only the finished style of the classical scholar, but the acute and accurate reasoning of the logician. His inductions are generally drawn in a strong and masterly manner, and as a polemical writer he uses his pen with much energy and effect in turning the facts or arguments of an antagonist against himself.'" There is a suggestion that this quotation forms part of the plaque mentioned earlier but that has not been confirmed and Captain Lawrence-Archer only recorded the part quoted above.

Edward married Ursula Hill Hoseason, daughter of William Hoseason and Maria Hill, on 6 Oct 1812 in Kingston Parish Church, Jamaica.¹ (Ursula Hill Hoseason was born on 5 Oct 1788 in Spanish Town, Jamaica ²⁵, baptised on 3 Dec 1788 in Parish of St Catherine's, Jamaica,²⁶ died on 31 Jan 1830 in Kingston, Jamaica ²⁷ and was buried on 1 Feb 1830 in Kingston Parish, Jamaica.)