It depends on how much ‘tech’ and ‘gnar’ you are going to do. If you are riding along rocky trails that are jeep tracks in the hills, then a sub £500 bike would be fine. But once you start throwing it down singletrack, you need something different.
My daughter’s Whyte 603 was £650 and I wish it was my size cos it’s begging for a bit of proper singletrack shredding. It’s heavy, has 2×10 and a coil fork, but the fork seems well enough made and has adjustable damping, but the geo and setup is bang on. I don’t think anyone shelling out on that would be disappointed.
Most of the bikes we looked at under that price, the £4-500 range were reasonable in terms of quality but they had more pedestrian geo and whilst fine for general riding around off road would not be as rewarding or fun on anything technical.
Having said all that, you probably would need to budget for tyres since most bikes (including the Whyte) don’t come with gnarly mud tyres that would suit winter riding in some parts of the country. In others they might though, depends where you are and what your trails are made of.