I am currently asking for similar help in the Ireland and Scotland forums and this will be the third part of our trip. We are a family of three including our 5 year old dughter who is a great road-tripper. Our England trip start with us arriving is Keswick driving from Oban that day. Please let me know your thoughts on this itinerary.
Day 1: Arrive in Keswick (stay Keswick)
Day 2: Lake District (stay Keswick)
Day 3: drive to York (stay York)
Day 4: York (stay York)
Day 5: Drive to Warwick Castle and spend day there (drive to Bath that evening)
Day 6: Bath (stay Bath)
Day 7: Stonehenge then drive to London
Day 8-11: London and side trips
I realize Day 5 is 5+ hours of driving so another option is to stay near Warwick Castle that night. That said, I would prefer to wake up in Bath in order to have a full day there. Less time in London is not an option as my wife will be at a conference three of those days.