This Nursery Rhyme was written in 1680 by the satirical English poet Tom Brown (1663-1704). Whilst Tom Brown was a student at the Oxford university of Christ Church he got into some trouble and was sent to the Dean - Dr. John Fell.
Dr. Fell (1625–1686) was an English clergyman, the Dean of Christ Church who later became the Bishop of Oxford. Dr Fell was furious with Tom Brown but before expelling him he set him a test. If Tom passed the test, to assess whether he could use the literary style marked by the use of epigrams, he would not be sent down. The test was to further translate and extempore work by Martial, who was the most well-known of Roman epigrammatists. Martial's epigram was in Latin as follows:

"Non amo te, Sabidi, nec possum dicere quare;
Hoc tantum posso dicere, non amo te."

Brown made an excellent English translation:

"I don't like you, Sabidius, and I can't say why; all I can say is I don't like you"

Tom Brown used this as a basis to then compose the witty nursery rhyme 'I do not like thee, Doctor Fell'. The nursery rhyme 'I do not like thee Dr. Fell' was not included in Mother Goose collections until 1926, following the rhymes inclusion in 'Less Familiar Nursery Rhymes' by Robert Graves (1895 - 1985) the famous author of 'I Claudius'.