When Bulgaria joined the EU it made an exemption for foreigners buying agricultural land for seven years. This time has now passed and whilst non-EU citizens are not allowed to buy agricultural land, citizens of the EU are (https://www.ruskov-law.eu/bulgaria/arti ... garia.html
Of course, being British this will not last long for you, so I would suggest that if you're going to do it you do it soon.
That said, you will not be able to build anything other than a very rudimentary structure without planning permission and land regulation. Even if you're not on the grid and don't have foundations etc you will still be deemed to be 'inhabiting' as if it is a house and you will get problems. Quite apart from the fact that when its -20 for a month and you're under 3 feet of snow 5 miles from anywhere you will wish you were in a proper house. Or you'll be dead.
Without meaning to be overly patronising, all these guys you see on History channel doing their 'back to the woods' existences are being paid vast amounts of money and go back to civilisation in the winter. They never show how utterly bored and miserable people are throughout the winter in northern climes, just like they rarely show the bazillion mosquitos biting everything all summer.
In summary, you can buy a place, you can build a 4 walled shack with a roof but if you try and live in it you will get some local Bulgarian official hassling you in a language you don't understand. He'll probably be drunk and have a gun. I won't even start on what the gypsies will do to you when they find you're building a place there.....