A quick look at the options seems to indicate it would be: drive or fly to Heathrow, then via Vueling to La Coruña; or ferry from the south coast to Bilbao, then train or hire car.
Can anyone think of anything else? Any organised tours? Not keen on cruises – never tried them, but the idea doesn't appeal; and not keen on connecting flights – pushes up both the travelling time and the cost. But we're willing to consider most things :)