buckyb
The surname Thompson was present amongst England's Romany population from the late Tudor era, being first noted in East Anglia in the 1590s. Below are the records I have identified for them in the following centuries:
17th century = Yorkshire x 2, Surrey, Cambridgeshire, Leicestershire, Shropshire
18th century = Hampshire x 6, Surrey x 2, Cambridgeshire x 2, Nottinghamshire, Staffordshire, Leicestershire, Yorkshire, Suffolk
19th century = Hampshire x 5, Essex x 4, Sussex x 2, Dorset x 2, Gloucestershire x 2, Norfolk, Somerset, Leicestershire, Yorkshire, Nottinghamshire, Kent, Surrey
20th century = Hampshire x 4, U.S.A x 4, Dorset, Gloucestershire,
As you can see from the mid-18th century they were particularly associated with the New Forest in Hampshire, but were still noted travelling in many other English counties, including Somerset, and by the 20th century were also travelling across the U.S.A.
I think it would be impossible to identify your Thompson's as Romany people just on your DNA results, but that said if you do show some South Asian, but no African, it does raise the possibility certainly. I have two or three other examples of Romanies described a 'Negroes' or 'Black men' in late 18th century and early 19th century records. A clerk may have described them in such terms if they were particularly dark skinned.
Do you have your Halpogroups? If this is your direct paternal line, father to son, your Y Haplogroup might provide some extra information. H1a1a-M82 is particularly associated with European Gypsies. It almost certainly originated in the earliest Indian populations, and is still seen in rates from 80% in Eastern Europe, to around 25% in Western Europe. It is not usually found in other Europeans. The absence of the Haplogroup of course doesn't disprove Romany ancestry, but the presence of it is a big indicator. In that respect it might be more use to you then the autosomal ethnicity estimates.