An old article from Andrew Marr, but a wonderful quote:
But if British-Americanism is intense, it also offers an interesting lesson for the rest of the world: for the corollary seems to be an equally intense desire to assert a different identity, too.
You find it in humour, in sport, in the monarchy (far stronger than most people would have predicted a decade ago). You will see it in Britain's newspaper culture; in soap operas and the tone of British television news; in the mere existence of Radio 4, which is perhaps the most un-American act carried out daily in English; and in the generally far less religious atmosphere of modern Britain, a secular, indeed godless place by American standards.
Radio 4 is arguably the height of modern civilisation, even americans (poor dears) can get it via the wonders of the interwebsuperhighwaynets. Need not fear, my merkin chums, by un-American, the author means unashamedly British.
My personal recommendations, the comedy, the current affairs, and occasionally the 'magazine' programmes. Desert Island Discs is good, and Woman's Hour is listenable even for blokey blokes. I tend to steer clear of the drama, not my thing on the radio.
For the Comedy, look for 'The News Quiz', 'The Now Show', 'Just a Minute' and 'I'm sorry I haven't a clue'. Other stuff can vary in quality, but these are universally excellent, the latter two are possible quite gentle for some tastes.
For politics, look for 'The Today Programme', 'Any Questions', 'Any Answers' (if you listen to Any Questions), 'PM' oh, and 'The News Quiz'!