I've had excellent experience of Goodyear Vector 4 Seasons. I drove straight up a 1-in-3 hard packed snow covered indoor ski slope and they were also good on summer roads, with plenty of ‘feel.’ Best information at www.tyrereviews.co.uk/. You'll probably need to go down to 16-inch wheels to get Vectors to fit.

Update: JS later wrote to tell me that event-tyres.co.uk had done a brilliant job fitting the Vectors at a very sensible price.