I'm not sure why Elvis68 would want Parkie to interview Churchill. He was a notoriously boring speaker in the House of Commons - I doubt that he'd provide 'laugh a minute' entertainment ;-)
Dead: Alan Coren (one of the wittiest Britons of recent years), P G Wodehouse (for some serious conversation addressing his alleged Nazi sympathies plus some moments of humour), Sid James (to explore his connections with the East End crime gangs plus plenty of humour) and Peter Jones (the actor, not the businessman - a natural raconteur).
Living: Even though I'm a republican, I have to agree with Elvis68 that the Queen might make a good interviewee - but only if she'd been treated to plenty of (alcoholic) 'hospitality' first, so that she'd 'drop her guard' when questioned ;-) Also Adrian Chiles (intelligent and witty - although, given that he's half Croatian, he might not be living much longer if certain England fans get hold of him!), John Sergeant (an intelligent and witty raconteur) and John Sessions (one of our most talented actors).
Chris