London to Lake District?

Avanti West Coast train from London Euston to Penrith every hour, in just over 3 hours. Bus X4 or X5 every 30 minutes from Penrith Station to Keswick, 45 minute journey.
On a good day a 4 hour journey end to end.
For Windermere change off the Euston train at Oxenholme for the Windermere Shuttle train. Overall journey time about 3:15

If Carlisle Airport ever reopens post Covid then flight from London Southend Airport (frequent train from Liverpool Street to the front door of Southend Airport).
Free Shuttle bus Carlisle Airport to central Carlisle, bus to Keswick

This forum was extremely helpful in finding the best transportation from London to Keswick. However, I will add that it is a good idea to buy your train ticket from London to Penrith in advance, because the reserved seats on the train are apparently sold quickly. Finding seats on the "open/unreserved" car seating of course can be done, but it can be harried and a bit stressful at the very busy London Euston station platforms. The London to Glasgow (with a stop in Penrith) is a well-used train route filled with locals that goes to northern England stops and on to Glasgow. By buying reserved seats in advance, you'll start your trip in a more relaxed frame of mind.