Self Drive UK, Wales

First of all, I strongly suggest that you arrange to drop off the car somewhere other than London and then take public transport into the city. Why? Because driving into London is not only difficult in terms of traffic, traffic congestion and parking but can also involve payment of a congestion charge:
https://tfl.gov.uk/modes/driving/congestion-charge
As you want to visit Wales (I think?) it would make sense to drop off the car somewhere like Bristol (train into London) or Oxford (train or long-distance buses). UK public transport may not be particularly cheap but it is safe, comfortable enough and reliable.
www.nationalrail.co.uk for train times, details and fares. 
www.nationalexpress.com , www.oxfordtube.com and  https://uk.megabus.com/  for long-distance buses.
Eighteen days is a good length of time to make the drive. For routes, have a look at the AA website. The AA is one of the UK's two major motoring organisations and its routeplanner will give you route, estimated drive times, route details, route alternatives and info about e.g. roadworks.
http://www.theaa.com/route-planner/index.jsp
Do be aware that UK roads are congested, even motorways, and that rural roads are often narrow and winding with little chance to overtake slow-moving traffic such as tractors. Rain also slows everything down, everywhere. So expect all journeys to take longer than even the AA site suggests and be pleased if they don't!
For accommodation look at www.booking.com which is thoroughly reliable and has very extensive UK listings, including many b&bs.
If I were making this drive I'd include:
Berwick-upon-Tweed and then Lindisfarne, Holy Island (stay overnight on the island).
Drive across the country along the line of Hadrian's Wall from Newcastle Upon Tyne to Carlisle, visiting the many excellent Roman sites as you go (I particularly recommend Chesters Roman Fort, Vindolanda, Hadrian's Wall & Housesteads Roman Fort and Birdoswald). Break your journey in Hexham (wonderful Medieval abbey) and then in Carlisle.
From Carlisle explore a little of the Lake District, perhaps basing yourselves for a night or two in Kendal or Keswick.
Then onwards to Chester (England) for an overnight, its cathedral, its Medieval 'Rows' and its Roman remains.

From Chester make your way along the North Wales coastline, taking in at least Conwy and its excellent Medieval castle and Caernarfon with its even better Medieval castle. Stay in Caernarfon and make a daytrip to nearby Llanberis, at the foot of Mount Snowdon, for its lakes, its superb slate museum, its amazing hydro-electric scheme and the little train which goes almost all the way up Snowdon. You could easily spend another whole day exploring more of the Snowdonia National Park .

From Caernarfon drive down the west coast of Wales, taking in Portmeirion (where 'The Prisoner' was filmed) and/or Harlech and its fantastic castle before breaking the journey in Aberystwyth.
From there, carry on along the coast towards lovely Pembrokeshire and tiny St David's , the UK's smallest city. Break your journey in that area to explore the beautiful coast and countryside.
From St Davids to Carmarthen and then the wild and beautiful Brecon Beacons. Overnight in Brecon and then onwards via Abergavenny to stay for a couple of nights in e.g. Cwmbran or Newport (Wales). Make a daytrip by train into Cardiff, if only for its excellent castle. 
From that base, drive to Gloucester (England) (Medieval cathedral, lots of history, super dockside development) and then either to Bristol (also a super dockside development + the Clifton suspension bridge) to drop the car or onwards via Bath and Stonehenge to Oxford.
Of course, if you want to see more of England you'll have to vary your route. The trouble with the UK is that all four countries really are stuffed with history and umpteen places to visit. I'm afraid you'll be spoiled for choice!
I'll shut up now.........  Enjoy your planning! :-)