You can definitely have a nice house to live in with a £50k budget.
Actually the first property I bought was like your description - complete with hole through ceiling to the sky.
I was lucky, the cause of the problem was not too serious.
Many years later I met my husband (a plumber) and our business does house or room renovations all year round for home-owners like you.
The first and most important thing you should do is get 3 quotes for the roof repairs. Not from general builders but from established local roofing companies - with good reputation and decades of trading history. Get these ASAP.
Then if the house is empty you MIGHT be able to get access to do the roof repairs after contracts exchange but before completion.
You might need timber treatments in the loft, perhaps repairs/replacement... so could be any price - you need experts to look at it.
This all needs to be done then you know what you've got left to spend on everything else.
Repairing the ceiling - replace it, plaster it, paint it. No problem for the professionals - not a DIY job (the painting can be).
Prices: for a complete bathroom refurb all done by professionals (like us) it should take 2 weeks and typical price is £8-£10k. You can cut this down a little depending what you want but equally you can easily double this price with lovely fittings, lovely tiles etc. Similar applies to kitched refurb.
Again look for companies that specialise in this work.
If the property is empty you can't really test heating until you move in. If it is an unknown quantity if will be worth asking a heating engineer to check out the heating system when you move in (A Home owners gas safety inspection - could cost about £60-£80). The boiler might be newish but if the rads are pre-2000 it is definitely worth replacing them with the best newest (Stelrad). New rads are designed differently have less water and are cheaper to run. you might not necessarilly need the same size rads - so talk this through with reputable & experience heating engineer.
If you can afford to pay one company to get on and do the work it could take just weeks (perhaps 4-6) depending on how big the house is and how many bathrooms?