London to Cumbria ~300mi - Any route planning tips?

If you go through Derbyshire, want to avoid hills and you have 25 or 28mm tyres on I would tip you towards the Tissington Trail, steady slight incline from Ashbourne town centre to just short of Buxton. Can get a little dull but there are some good views as you get further north and it does flatten out the county (the White Peak part anyway).

As luck would have it, I have a good friend who lives in Ashbourne with plenty of spare rooms in his farmhouse.