BBC Radio 4, closely followed by Radio 2.
Subject says it all. I like Radio 4 for these following reasons:
1) "Today". This morning news magazine progam is the best; think of it as NPR's Morning Edition on steroids. Politicans get raked over the coals (all political parties get the same treatment) by no-nonsense, take-no-prisoners jouralists like John Humphries and James Naughtie. No jingles, no music (unless you count the Greenwich Time signal at the top of the hour), just pure news & comment. American politicans: think yourself glad that there isn't a Radio 4 over here.
2) Variety of talk. You get phone-in's, discussion shows without phone-in's, plays, comedies, dramas, quizzes, serious news, science shows, women's issue shows, gardening shows.
3) Heritage. Radio 4 takes its heritage seriously. This is a very 'conservative' station, when anything drastic changes to the schedule it is usually complained about quite vociferously in the press the next day. A lot of shows are shows with a long history and are entrants in the Guinness Book of Records ("Desert Island Discs" - longest running record request show, and "The Archers" - longest daily serial drama to name of two shows I know are in the Guinness Book of World Records).
4) Interesting stuff to listen to. You may not be interested in women's issues, but Woman's Hour is for me interesting to listen to. Whatever is on, you can usually get into what's being talked about very quickly.
Now as for the #2 choice: BBC Radio 2. Some of the same reasons remain, but it's basically because it does evolve with the times, it has brought its music more "up to date" but not as cutting edge as Radio 1. It has its specialist shows for Big Band and older styles of music. Country isn't big but Radio 2 has its country specialist shows. Its personalities are genuine people who are loved by their audience. Terry Wogan gained popularity doing Radio 2 for breakfast, left to do TV for a while, and after his TV show came to an end he came back to Radio 2 in the breakfast slot. He's the #1 presenter in the UK. Jimmy Young had been for years on Radio 2 but people were most displeased with the manner in which he was "eased out" of his job. However, the rising star at Radio 2 lately has been Jonathon Ross - who has a problem in pronouncing 'R's. I remember him trying to say on TV (before his R2 days) "We have a lot of top rank entertainment for you tonight"... change that r to a w in 'rank' and you get a more accurate picture of what I imagine him to sound like. However he is intelligent, thought provoking and quite often amusing. Some think he's going to take over Wogan's slot if/when he retires.
Honorable station mentions go to Radio 1, 96.4 The Eagle, BBC Southern Counties Radio and WUNC.