Having walked both Offa's Dyke and the Pennine Way, which follow the borders between England and Wales, and England and Scotland, I couldn't possibly guess how many times I have been to the three nations on the mainland of Great Britain.
I have been to the Channel islands three times, visiting five of them in total. (technically there are two dependencies, Jersey being governed separately from the rest). Also been the Isle of Man and Northern Ireland, but the Republic is one of ten EU countries I have yet to visit. (the others are the Baltic States, Denmark, Finland, Croatia, Poland, Bulgaria, Cyprus and Czechia (although I was there when it was still part of Czechoslovakia). I haven't kept a tally of those I have visited though.
I visited both Slovenia and Slovakia both when they were respectively part of Yugoslavia and Czechoslovakia, and again after independence, so I'm not sure how to count them.
Outside the EU I have been to Russia, Ukraine (2) and Moldova (when they were all still part of the Soviet Union), Turkey (2), Egypt, Morocco, Switzerland (6) and Liechtenstein (but only passing through non-stop on the train)