If you are driving back to London then I think it is worth taking the M6 Toll road.
Down the M6 to Junction 11 then onto the M6 Toll. For the extra £10 or so I think it's worth it. Then (and again this is subjective) when you come off the toll take the M42/M40/M4 route rather than the M6/M1. That will take you straight to Heathrow where I assume car drop off is. Good luck with that, maybe on a Tuesday it won't be too bad.
On arrival day I find it difficult. The easy way is straight down the A30. But I would love to say to you to take the route down the coast to see the Cornwall you have come to see- through Holywell Bay, Perranporth, St Agnes, Porthtowan and Portreath. On a summer Saturday that is likely to be slow going. At least you drive on the same side of the road as us. But apart from traffic some of the roads down the coast are decidedly skinny, and you certainly need to know how to reverse in a straight line.
St Ives to Lynton is every bit of three hours on the main road. I would say to have stop offs in Okehampton and Launceston on that route. I am not sure whether to say to come off the A30 at Bodmin, then up the coast via Port Isaac, Tintagel, Bude, Hartland Point and Clovelly on the A39. I'm just worried it adds too much time onto the drive (and time off Lynton), even if it is the scenic route.
Lynton to Bristol is 3 hours on the A39 along the coast, which is not the fastest route but is the route you must take. In July I think you add an hour onto that. More if you want to add in Dunster Castle or Taunton. You don't have time for both as you also need the afternoon for the sights of Bristol (and next morning).
Hay on Wye to Liverpool- I've mulled this over as there will be different opinions over this. I think I would take the A483 up through Builth Wells and Llandrindod Wells through Newtown then Welshpool. You could overnight in Welshpool but personally I would add the extra hour over B roads to Bala for your overnight. [Disclosure I have historical family links in Bala so am not impartial]. But it is undeniably beautiful up there.
Then next day the A494 up through Corwen and Ruthin.
I would then take you up the west side of the Wirral Peninsula - Heswall, Hoylake etc for the Mersey Tunnel to Liverpool.
But I accept that you probably won't be able to avoid the call of a stop in Chester (use the Park and Ride into the City). Afterwards take the M53 and Mersey Tunnel route to Liverpool.
If you overnight in Welshpool then take the A483 through Oswestry, Chirk, the famous Pontcysyllte Canal Aqueduct and the Wrexham Bypass to Chester.