You can find little pockets of ‘wild’ in almost any part of the country. But they will be little. I fly for a living, and it’s always a surprising thing just how rural Britain looks from the air as soon as you set foot outside the M25. I also take part in a couple of adventure sports, and am always looking at places from the pov of ‘ooh, this place would be great for that sort of competition.’
I could list places but that wouldn’t help you - if you need to be in London for work your ‘2 hrs away’ is going to be very different depending on the nature of your commute. I work at Heathrow, and live in a very wild (but little) place about 40 mins drive along the motorway. But I also sometimes have to go to Gatwick and that takes nearly 2 hrs. DH sometimes works in Greenwich, for that you have to allow 3 hrs no matter whether you drive or take public transport (it can be done in less but only if all the stars align!) DH can get to Paddington from ours in only 35 mins though.
If I were you I would make the bit of London you want to be within 2 hrs of your staring point then find the furthest places you can make the journey from in 2 hrs, and make that your search area. Within that you will find lots of wild. Within my circle of one hour from Heathrow, for example, would be Bracknell Forest, parts of the South Downs, Lambourn and Marlborough Downs, Surrey Hills, even the edge of Salisbury Plain. I could take you, as an adventure racer, and get you lost in any number of those places! (I got a bunch of competitors lost in deep forest only 30 miles from London earlier this year in a place they thought was a bit tame till they got there!)
There are beautiful places, but you have to keep your ideas small (we do, after all, live on quite a small island) as if you wanted endless miles of wilderness you really would need to be looking much further north. Even Dartmoor looks very small when you fly over it compared to the endless forests of France and Germany. (Although flying over eg Belgium you wonder where they’ve put their countryside!)
I know you are looking for ‘remote’ and rural, but it is worth bearing in mind that by moving yourself you will add one more tiny change to an area. Where I live we had a fabulous rural pub. It had 2 rooms, one for locals (where, as an incomer, I would not dream of sitting) and the other for incomers, walkers, cyclists, riders. When the old landlord retired it was bought by a TV chef and transformed into a remote gastropub within 2hrs of London, marketing itself as the sort of non-manicured place you could eat wild game. It’s not a village pub any more, it’s become a pastiche, exactly the sort of place London people come to because they think it’s not one of those other manicured places. I’m probably not explaining it very well. But if you want to be somewhere remote but commutable to the Big Smoke, it will already be full of commuters.