Edmund was the son of Rev. William Dickinson, Rector of Appleton Church in Berkshire, by his wife Mary, daughter of Edmund Culpepper. He received his primary education at Eton, and in 1642 entered Merton College, Oxford, where ho was admitted one of the Eton postmasters. He took the degree of B.A., graduating on 22nd June 1647, and was elected probationer-fellow of his college, "in respect of his great merit and learning." On 27th November 1649, he had the degree of M.A. conferred upon him. Applying himself to the study of medicine, he obtained the degree of M.D. on 3rd July 1656. About this time, he made the acquaintance of Theodore Mundanus, a French adept in alchemy, who prompted him to devote his attention to chemistry. On leaving college, he began to practice as a physician in a house in the High Street, Oxford, where he "spent near twenty years practicing in these parts". The wardens of the college made him superior reader of Linacre's lectures, in succession to Dr. Lydall, a post which he held for some years.

Dickinson was elected honorary fellow of the College of Physicians in December 1664, but was not admitted a fellow till 1677. In 1684, he came up to London and settled in St. Martin's Lane. Among his patients here was the Earl of Arlington, lord chamberlain, whom he was fortunate enough to cure of an obstinate tumour. By him, the doctor was recommended to King Charles II, who appointed him one of his physicians in ordinary and physician to the household. The monarch, being a great lover of chemistry, took the doctor into special favour and had a laboratory built under the royal bedchamber, with communication by means of a private staircase. Here, the King was wont to retire with the Duke of Buckingham and Dickinson, the latter exhibiting many experiments for his majesty's edification. Upon the accession of James II (1685), Dickinson was confirmed in his office as King's Physician, and held it until the abdication of James (1688).

Being much troubled with stone, Dickinson now retired from practice and spent the remaining nineteen years of his life in study and in the making of books. He died on 3rd April 1707, aged 83, and was buried in the church of St. Martin-in-the-Fields, where a monument bearing an elaborate Latin inscription was erected to his memory.

While still a young man, Dickinson published a book under the title of 'Delphi Phoenicizantes' (1665), in which he attempted to prove that the Greeks borrowed the story of the 'Pythian Apollo' from the Hebrew scriptures. Anthony A’Wood says that Henry Jacob, and not Dickinson, was the author of this book. This was followed by 'Diatriba de Noae in Italiam Adventu' (1665). In maturer age, Dickinson published his notions of alchemy, in which he seems to have believed, in 'Epistola ad T. Mundanum de Quintessentia Philosophorum' (1686). The great work on which he spent his latest years was a system of philosophy set forth in a book entitled 'Physica vetus et vera' (1702). In this laborious work, on which years had been spent, and part of which he had to write twice in consequence of an accident by fire to the manuscript, the author pretends to establish a philosophy founded on principles collected out of the 'Pentateuch.' In a very confused manner, he mixes up his notions on the atomic theory with passages from Greek and Latin writers as well as from the Bible. The book, however, attracted attention and was published in Rotterdam in 1703, and in Leoburg two years later. Besides these, he left behind him, in manuscript form, a treatise in the Latin on the 'Grecian Games,' which Blomberg published in the second edition of his life of the author.

The diarist, John Evelyn, went to see Dickinson and records the visit thus: "'I went to see Dr. Dickinson, the famous chemist. We had a long conversation about the philosopher's elixir, which he believed attainable and had seen projection himself by one who went under the name of Mundanus, who sometimes came among the adepts, but was unknown as to his country or abode; of this the doctor has written a treatise in Latin, full of very astonishing relations. He is a very learned person, formerly a fellow of St. John's College, Oxford, in which city he practised physic, but has now altogether given it over, and lives retired, being very old and infirm, yet continuing chymistry."