The main issue will be finding good people who can do it on such a tight timescale. A good rule of thumb when employing tradespeople is that you can only ever have 2 out of these three things, good, cheap and fast. So if you want it done well and fast it will cost a lot more.
I think you are looking at £7000 to get a full new heating system including radiators and a boiler. And 5000-6000 for a full rewire.
That will involve taking all the floors up and channeling into all the wall though, so the house will be a mess afterwards. Everything will be covered in building dust and all the carpets will be dirty and need a serious clean or replacing. The walls will need at least patching or realistically skimming
Does the house need rewiring? Unless it is really old, you can probably get the fuse board and consumer unit upgraded to modern standards and then upgrade the wiring to each room as you work round and decorate them. Same with plumbing. You can get a new boiler and then do the radiators a room at a time. It is better to take them off for decorating anyway.
New windows will be around £500-£1000 per window and doesn't make much mess so that can be done at any time, even once you have decorated.
If you are renovating slowly and living in then it is best to make sure the house is watertight and insulated first, so I would prioritise loft insulation and windows, followed by boiler and electrical fuse board and consumer unit upgrade. These should be way to get booked in for the 2 months you have. Get recommendations from people at work or neighbours or family and be very wary of anyone who has quick availablity, rather than a spot in a month's time.
For wallpaper stripping, prepping and painting you would probably pay £1000 a room. However this is a really easy place to save money and learn some DIY skills. If the walls are not in great condition, you may end up having to get the rooms skimmed once you remove the paper and this could be £600-£1000 per room. You could easily strip and redecorate one room in evenings and weekends as a beginner diyer in 2 months, maybe 2 rooms of you are quick or could rope some help in.
For a new consumer unit and fuseboard , an electrician should be able to do that in a day and it might cost £600-£1000.
New boiler will be whatever the cost of the boiler plus maybe some new pipework so maybe 2-3 days of plumbing time (£800-1000) plus the cost of a boiler and parts (not sure about this but maybe £2000-3000?