Fly to Edinburgh and spend some time exploring the city. You won’t need a car here as public transport is so good (parking difficult and expensive). Hire a car when you are ready to leave Edinburgh. You have a choice here. Either then drive to Glencoe OR think about doing a day tour to Glencoe - Rabbies do one from Edinburgh and get consistently good reviews.
I reckon you have 8-9 nights to play with?
Hire a car from Edinburgh Airport. Then head south via Carlisle to North Wales. This will take a full day. Plan to stop in Llandudno (Victorian sea side town ) OR Conwy (Walled Medieval town with a ruined castle). They are only a few miles apart and make a good base to explore North Wales. Plan on 3 nights.
Then drive down through Wales to Cardiff for 3 nights. Either travel the coastal route or else down through the centre of Wales. Again Allow a full day for the journey.
Head to Bath (couple of hours drive) for 2 nights.
Then hand in the car and travel by train to London for the rest of the stay. Again you won’t want a car in London.