Hey, I'm Scottish but currently in Estonia. Is this specifically English law you are talking about? Because it sounds a lot more restrictive than Scottish law - you can basically camp anywhere without permission (except the eastern shores of Loch Lomond in summer months because neds/chavs always leave litter and other people's gardens, but it's fine if you ask, and currently used crop land, but you can go to the boundaries) and set a fire as long as it isn't in sight of a road.
And yes, land is too expensive in the UK, unless you can buy forest land in Scotland in bulk for a few hundred pounds per acre, but we're talking costs of upwards of half a million so it's not feasible. There is an option to rent fields for nominally for horses, which is usually super cheap. The restriction is contractually you would have to vacate the land a minimum of 1 day per year otherwise it cannot be rented as grazing land (presumably to allow it to recover...). I doubt that would be a problem though.
The note about travellers is correct - they still even have to pay rent to the local council if they can even find a spot to live legally, which are few and far between. I'm not sure there are even Highland Travellers anymore.
Another problem is hunting and gun regulations in the UK are quite prohibitive, for instance having to have a secured gun locker bolted to a brick wall. How can we have that if we are nomads? And not being allowed to cross other people's land with a firearm - how do we move between nodes? So getting calories from the land isn't such an easy task in the UK. Sea fishing and shore foraging for personal use is not prohibited in any way that I know of. River and lake fishing often needs a permit for the specific waterway in Scotland, which is super annoying, although some are permit-free. So an idea I had a while ago would be do nomadic sea kayaking between the western islands, Argyll and the western highlands. Many of the islands are uninhabited and the highlands are sparsely populated, some islands have feral sheep/goat populations and no law enforcement so no one would ever know if one went missing.
Problems with this style - holy shit have you ever been to the western islands of Scotland? There is nothing but the Atlantic between them and North America. It is so stormy and wet. Not so cold, it barely snows or freezes anymore. And climate predictions say it will only get wetter and stormier. The weather can change in the snap of your fingers, you think it is bad on the mainland? It can be 26C and a clear sky then nearly a hurricane with pissing rain in 30 minutes. On Tiree, the sunniest place in the UK, plants grow to the north east because of the wind. We'd need to keep our storm clothes on or close by otherwise it can get tricky. But we'd have no need for buying land or dealing with permits or the law so it has its ups and downs.