We did something similar Sept / Oct last year. The following maybe useful
We took the train from London to Edinburgh. Nice scenery pretty much the whole way.
Two nights in Edinburgh was sufficient for us as it's not that big. We stayed at Gleneagles Townhouse (excellent). Recommend doing The Water of Leith walk (stunning)
We then hired a car for 13 days and took the long way to Heathrow. Ended up getting upgraded into a GLE450D SUV as they were keen to get the car back down to London town. We went with Sixt as they were half the price and had unlimited milage included. Milage is important as we ended up clocking up around 2300 miles over the 13 days. The GLE450d is kinda big and it handled the conditions very well throughout Scotland, England and Wales. We travelled hundreds of miles on one lane roads with tiny passing places - no worries.
We headed North with stays at Braemar (2 nights at The Fife Arms - excellent), Tongue (2 nights at Lundies House - beautiful), Skye (2 nights at Kinloch Lodge - great history), Loch Lomond (1 night at Cameron House - big). With all these stays in Scotland we did many outings in the car and really got to see the local area.
We then headed to the Lakes District and based ourselves in Cartmel (2 nights at L'Enclume - this was outstanding and very, very special - great lodgings and superb food!) Again we did trips in the car and travelled all over the district.
It was then Wales as we'd never been before with a 2 night stay at Narberth (Grove of Narberth - beautiful). Again the car got a workout seeing the local area.
Headed to Heathrow with a one night stay in Oxfordshire staying at Le Manoir aux Quat'Saisons - an absolutely beautiful property within striking distance of Heathrow and Windsor. The meal was sensational and with a 4pm checkout via Amex the breakfast, property, and local area could be enjoyed before our 8.30pm flight to Singapore.
We did drive through Glasgow and thought is was definitely worth visiting next time.
Sixt was ok, particularly their return area being right smack in the middle of terminal 2. You need the usual - passport, license, credit card you made the booking. We ended up needing to put Adblue, oil and air in the car which was all refunded minus the usual bank transfer fees. The car was new, but still required about 100GBP worth of stuff.
Scotland is very different to England, you can see there's not much money spent on general maintenance or infrastructure, but it was stunning and well worth heading north into the highlands.
There are cameras everywhere, and they work unlike Italy / Europe! Ended up collecting three fines - bridge toll, 24hr bus lane in Glasgow, and doing 28miles in a 20 mile zone in Wales. Wales only dropped their speed limit down to 20 from 30 days before I turned up. Sixt slugged me a 40GBP admin fee for every fine - I still had to pay the actual fines.
The SUV was perfect and handled all conditions and areas easily. Given the amount of driving we did it was nice to have a bigger / higher car.
Enjoy!