Remoteness

In Britain the two contenders for furthest spot from a road is 2.4 miles at Riggs Moor in Yorkshire Dales or 5 miles from a road at Hells Bottom on Glendhu Hill in Northern Pennines in England, or 5.7 miles from a road at Fionn Lock in Scotland, or 3 miles from Glynatawe in the Black Mountains in Brecon Beacons in Wales.

There are of course areas that feel like wilderness due to inaccessibility, naturalness (eg self seeded vegetation and absence of human structures) or lack of settlement, such as those found in North Pennines, Lake District, Scottish Highlands and mid Wales.
If you can see buildings, tilled soil, grass or coniferous or deciduous trees you are not remote – for that you tend to need to venture into scrubland, which usually means mountains or moors.
Remoteness from population in Britain only begins as you move north west, and if you are within 50 miles of the M25 you are as unremote as it is possible to be, although East Anglia is as good as the rest of Wales and Scotland.

Roads everywhere!

To escape roads and signs of civilisation it helps to be near the coast but your best bets are in Scotland, mid Wales, North West England and Dartmoor.

England is rammed with roads and has only a few national parks where you could get an hour’s hike from a road. Much of Wales looks natural but is really just a stroll from roads and villages. The biggest gaps between roads are around mountains and are about 5-10km as the crow flies, meaning you are as little as 2.5-5km walk from the nearest road. Scotland has some slightly more remote mountains but never more than a few hours hike, and you have to cross a wall of roads across Edinburgh and Glasgow to get into Scotland, and Wales is similarly fenced in by a mass of roads.

You are never more than a day’s walk over rough ground from population or roads.
As at 2018, 83% of the UK lived in urban areas, so all rocking up in rural areas and expecting spare housing or even not to be noticed in the woods is impossible. So you cannot be too far to find, and thus have to concentrate on being too camouflaged to find or too discrete to notice or too secure to be invaded.

Tips for going on the run

For example, Essex is 60% denser than national average yet is a rural county with 72% of land used for agriculture, so if all the townies headed for the hills it would be like a rave on a farm, with 560 people per square kilometre of field, each having a plot 42 metres square – like the length of a typical early 20^th century terrace garden, or one sixth of a football pitch each – hardly invisible.
In England average population density in 2021 was 434/km² or three people per football pitch side area, so 2,304 square metres each if they were to spread out, but again, if they all headed for the countryside then, although city dwellers would have more space than they do now, it would be more like 1,000 square metres each or a square plot 100′ x 100′. So you can’t all hide in the UK. If you want space you might want to head for Rutland where it is some 600 times less dense than Tower Hamlets with one resident per football pitch sized area. Or even better or worse, get a boat to the Isles of Scilly where all 2,100 of the the locals will notice you but it is even more spacious than Rutland. Another option is the City of London which is second only to the Scilly Isles for spaciousness as hardly anyone lives there, so taking over offices may be worth considering if you want to stay in London after a disaster.