No, not the television comedy sketch show Little Britain, but An Bhreatain Bheag, which is Irish for 'Wales' but which literally translates as 'Little Britain'. When I came across the translation in an English-Irish dictionary, I immediately thought of present-day Ukraine, which before the 20th century was called 'Little Russia' (Malorossiya in Russian) - or, at least, the western part of Ukraine was. It would no doubt be insulting these days to refer to Ukraine as Little Russia, but even Ukrainians seem to have used it in previous centuries. The novelist Gogol, who was Ukrainian but wrote in Russian, uses the term Little Russia in the very first sentence of his Evenings on a Farm near Dikanka (Russian text here).
I suppose what Wales and Ukraine have, or had, in common was a big, powerful neighbour that didn't brook any nationalist aspirations in its borderlands, hence the epithet 'Little'. Ukraine, a name in use since the 12th or 13th centuries to refer to various bits of territory around Kiev, literally means borderland (krai is edge or border). Wales derives from an old Saxon word meaning foreigner, Roman or Celt. The Welsh word for Wales, Cymru, derives from Old Welsh and probably means compatriot, according to the OED.