Car rental companies have offices throughout the UK, you'd be able to get a hire car at Carlisle, which is the nearest city to the North Lakes. Europcar, Avis, Hertz all have offices in Carlisle, close to the railway station. It's not the nicest drive from London to Carlisle up the M6, the train would be much nicer, but it depends on budget.

In terms of accommodation, it depends on your budget. At one end of the scale you've got somewhere like Armathwaite Hall by Bassenthwaite and at the other you've got little farmhouse B&Bs in the small fell villages.

You'd probably want at least two days/three nights to really see what you've come to see, the roads are very slow in the Lakes and you can't get anywhere in a hurry.