That's the claim in Stuart Laycock's book 'All the Countries We've Ever Invaded: And the Few We Never Got Round To', with a link to the map and news article here: http://www.telegraph.co.uk/history/9653497/British-have-invaded-nine-out-of-ten-countries-so-look-out-Luxembourg.html.
It sounds like very imaginative counting to me but I've never read the book. What do people make of the claim?
The author has a pretty broad definition of "invasion". He includes any British military presence in the country, as well as incursions by British pirates, privateers, and armed explorers.
A narrower definition of "invasion" would reduce the number of countries quite a bit, but the total would still be impressive.