Road trip recommendations for Normandy, England,Wales and Scotland

Allowing for 7 days in France, 3 days in London and at least 3 days for the Dover to Falmouth segment you've really only got 2 weeks and a couple of days to explore the UK. So, unless you're willing to fly e.g. from Newquay to Edinburgh, you've really got to cut down on the places you want to see.
Note that Leeds Castle, though pretty, is not Medieval. It mostly dates from the 19th century!
I've posted separately to explain about driving in the UK and why map distances are only a very rough guide when planning a trip. Our congested roads mean that trying to include Scotland as well as the other places you mention is a bit of a stretch, unless you simply want to (figuratively) whizz around and 'tick boxes'. I suspect you don't want to do that so I suggest you (sadly) cut out Scotland on this trip.
Allowing for your interests and time constrictions I'd suggest this potential itinerary. I've tried to stick to no more than 3 hours' driving between each place. 
Falmouth to Bath and overnight there. (1 night)
From Bath across the Severn Bridge to Chepstow and from there to Hereford for overnight (and wonderful Medieval cathedral). Take in Tintern Abbey en route if you have time. Pembroke (Wales), though lovely, is simply too far away to be included in this timescale. (2)
Hereford to Harlech (fantastic castle) then drive on an hour or so to Caernarfon. Overnight there. (3)
Caernarfon to Chester (England) (fantastic Medieval cathedral, city walls, Roman remains), taking in the excellent Conwy castle on the way. Overnight in Chester. (4)
Chester to York. Allow 2 nights in York because a) getting there may be slow because of traffic congestion and b) there's simply so much to see: wonderful Medieval Minster, city walls, Roman remains, Viking remains (Jorvik), the Medieval Shambles etc etc. (6)
Now you have a choice for the next 6 days or so: either
a) work your way back down south via Lincoln (England) and perhaps Stratford-upon-Avon to include the Cotswolds and perhaps more of Devon, Dorset & Somerset (Plymouth? Portsmouth for the fantastic 'Mary Rose'? Lyme Regis? Avebury & Stonehenge?)
or b) Continue to work your way north up the east coast, visiting Alnwick (castle and lovely town), Durham (wonderful Medieval cathedral), some of Hadrian's Wall, the Holy Island of Holy Island (overnight there if the tides are right!) to Berwick-upon-Tweed and Edinburgh. There might even be time for a daytrip or two from Edinburgh before you get the the train back to London.
That's only a rough itinerary. The UK is so stuffed with historical sites & sites: there's simply too much to see in a short trip!
Useful websites:
Under-Channel Eurostar official site: https://www.eurostar.com/uk-en
UK official railway website: https://www.nationalrail.co.uk/
National Trust (owns many of the historical buildings 'with a roof'): https://www.nationaltrust.org.uk/
English Heritage (owns historical buildings 'without a roof' in England e.g. castles): https://www.english-heritage.org.uk/
CADW (owns historical buildings 'with & without roof' in Wales:  https://cadw.gov.wales/?lang=en
Scottish historical sites & sites in public ownership are owned/run by Historic Scotland: https://www.historicenvironment.scot/
and the National Trust for Scotland: https://www.nts.org.uk/

A few pointers about driving in the UK:
1. Don't be misled by map distances. Any road journey will take longer than the map suggests, sometimes much longer.Our roads are frequently congested, even motorways, and especially so at peak times (roughly 7-9 am and 4-7 pm). Roads in rural areas are usually narrow (one lane in each direction, sometimes just one lane with occasional passing-places) and often winding: overtaking slower vehicles (trucks, tractors etc) can be impossible for several miles.
All these things combine to make journeys longer than the map suggests and ...importantly.. they make driving much more tiring too, because the driver really must remain fully alert all the time. 
2. Parking in city and town centres (not 'townships'..we only have cities, towns, villages and hamlets!) can be difficult and is often expensive. Make sure you keep a good amount of loose change for parking machines: pound and 50p coins are the most useful, though it's a good idea to also have some 20p and 10p coins to hand as well. Make sure you stick to the time you've paid for: traffic wardens patrol car parks and fines for overstaying are hefty.
Don't risk parking on double yellow lines, in 'resident-only' parking areas or on single yellow lines outside the allowed times (there'll be a sign somewhere). There are a lot of traffic wardens around, and not just in city centres!
It's always best to find accommodation which offers its own parking, (it may not be free) though this will be more difficult in city and town centres.
3. There are a huge number of speed cameras. They're on narrow rural roads as well as dual carriageways and motorways. If you're caught speeding the fine and/or licence points are automatic and the hire firm will chase you for the money. So always stick to the speed limit!
4. Hiring a car for a one-way trip will add a hefty premium to the total hire cost. Not all companies offer one-way hire so you'll probably be stuck with using one of the more expensive multinationals: Hertz, Avis, maybe Enterprise or Budget. The company website will indicate whether one-way hire is feasible when you try to get a quote. Car hire is pretty tightly regulated in the UK so it's not a matter of safety, just of cost.
5. Avoid buying fuel on the motorways. Service station prices are much higher than elsewhere (the same applies to food and drink they sell).