Ours is nearly 500 years old, timber framed and thatched - we've just had tudor chimney rebuilt with neighbours and currently having back half of thatch redone. The builders / thatchers we've had out have loved it (one even made an offer to buy our neighbours one when I mentioned she was selling) and keen to work on it though you ideally need ones experienced with listed buildings and you need to know the rules yourself. The main issue is a lot of things need permission so you need to know the rules but we love it. It does require you to have time to look up rules, fill in forms, chase council and in general like for like is much easier to get permission for and sometimes the only thing you'll get permission for. Though we prefer it like that so all the houses round here look nice.
Taking on one that requires doing up I would be wary of unless it's liveable as is, permission can be slow - thatch and trees was around a month but chimney as was knock part-down and rebuild as someone had rebuilt it badly before was August to May. I would definitely get a full survey and read up on it. It also would be challenging if we went into another lockdown as last time the approved brick company closed for 3 months and you have to use exactly those bricks.