London: Heathrow (LHR) is the main long-haul hub. Gatwick (LGW), Stansted (STN), and Luton (LTN) have plenty of European and some long-haul flights—and often lower prices. Stansted and Luton are farther out, so factor in train or coach time and cost.
Outside London: Manchester (MAN) is the busiest airport outside London and has excellent European and long-haul links. Edinburgh (EDI) and Glasgow (GLA) are the main Scottish gateways. Birmingham (BHX) and Bristol (BRS) are good options for the Midlands and South West.
If you're touring the UK, flying into one city and out of another can save time and open up more fare options. Compare Manchester vs London, or Edinburgh vs Glasgow, depending on your itinerary.