You appear to have missed out the bit about how you intend to travel to these places. Your proposal is completely unrealistic, in fact I'd go as far to say pretty much impossible.
You want to visit York for two days, that's fine, that's the minimum time I would suggest to devote to York yet you want to travel to Manchester or Liverpool for a football match AND explore the moors!!! Watching my own team play at home, 15 minutes drive away can take up almost half a day, making your way through heavy traffic, finding somewhere to park, grab a pre match pint or two, make the way to the ground to be seated in sufficient time before kick off (don't expect to turn up 10 minutes before kick off and be seated in time!), watch the game, slowly leave the ground with the hordes and then make your way back to the car (if you want to do this via train expect it to be just as long). Where does seeing York fit into this? You won't be back until the evening! Either devote the whole two days to York or spend two days in Manchester or Liverpool and incorporate the football.
How are you getting to Bath? Where are you picking the car up from? You want to cover Stonehenge, Cheddar Gorge, Bath, Lacock and Castle Combe? in one day!!!! Whilst it's feasible you could drive from one to the other in a day you won't actually be visiting or seeing anything which begs the question, why? Likewise the rest of your trip.
I understand that this is your first trip to Europe but you need to know the realities. Don't look at Google maps and think, "yeah that's doable" because it invariably isn't. It isn't like driving in the US where I once drove 50 miles from Lake Tahoe to Reno just to go to a cinema because it was raining that day. That's equivalent to me driving from home to London just to go to the cinema, an inconceivable idea!
Your itinerary, as it stands, would be a miserable, tiring, frustrating and wasteful experience. Par it down, incorporate more two and three night stops and concentrate on one area or two. The UK has so much to offer in a reasonably small space that you can see and experience so much without tearing around the country.