If this was Cluedo I'd be offering "In the conservatory, over a dodgy step".
(what is that mark on the floor by the mop?)
£40k is going to get a hammering there. The kitchen needs doing, the bathroom needs doing, there's some moisture damage over the loo in the bathroom to be investigated (likely just be condensation/poor ventilation but you need someone to check), and you'll probably want to do something about the fireplace/plinth in the living room. Most of the carpets are either hideous or beyond cleaning from what can be seen in the photos.
Providing survey doesn't indicated that the roof needs any work (nothing obvious in the photo, but the property clearly hasn't had much love spent on it in a while) and your prepared to do the decorating yourself then your budget is tight but possibly doable depending upon local contractor rates.
I'd prioritise:
- Kitchen
- Bathroom
- Bedroom carpets
Then review where you are. It's not worth tackling the living room unless you can do it all in one. The fireplace needs to be seen in person to make a decision. But there's no point doing the carpet in there if you're going to tackle either the fireplace or the '80s fashionable brick plinth, which are jobs that would need the carpet doing/redoing after they're tackled. If you keep the fireplace but get rid of the plinth, that's a sledgehammer job you can do yourself. But it'll need a plasterer to tidy up the wall afterwards.