UK in the US

Recently deceased Corrie star Anne Kirkbride.

Since the '60s a number of UK comedies and dramas found their way across the pond to the US and Canada (both Commonwealth and via the US) mainly on NET the predecessor of PBS until 1970 when NET were absorbed by flagship WNDT in New York to become WNET.  The BBC launched Lionheart Television (now BBC Worldwide Americas) which handled distribution and syndication with PBS member stations as PBS are technically the pubcaster for the US though not a de facto per se like Auntie (BBC).  Monty Pythons Flying Circus, Butterflies, The Good Life (as Good Neighbours to avoid confusion with another show), Are You Being Served?/Grace and Favour (AYBS Again US), A Fine Romance, Prime Suspect, Absolutely Fabulous, Some Mothers Do 'Ave 'Em, Only Fools and Horses, To the Manor Born, Eastenders, The Vicar of Dibley, Last of the Summer Wine, Keeping Up Appearances and Waiting for God (the last two I watch) just to name a few are or have been on participating affiliates but as an extra package as they're not network package shows like Downton Abbey (from ITV) and Call the Midwife are which give PBS ratings on par with their commercial competition yet air in North America several months after the UK depending on the show.
In markets bordering Canada or other select areas, if you can get the CBC on cable or over the air Coronation Street from ITV airs Sunday Mornings. Supernanny, Jeremy Kyle, Trisha Goddard and even Ant and Decs Wanna Bet? have all had brief US editions.
Ex-pats and diehard fans alike who can afford it can subscribe to an expensive satellite service which allows one to receive BBC 1-3, Channel 4, Five, itv, BSkyB and other UK networks but will still have to pay the licence fee and have equipment to rent to convert PAL signals to NTSC I would have to believe.
Some have had mainstream success Stateside while others have a cult following compared to back in Britain.  On cable BBC America only has a handful of Beeb programmes in order to appeal to US tastes making it BBC in name only if you ask me.