What kind of costs am I looking at for these internal works?

[ThisMustBeMyDream]

I've viewed a house today that is 40k less than another house I already have a sale agreed on (but it's been 5 months and they haven't found anywhere else and my buyer of 1 month is threatening to pull out if they don't find somewhere within 2 weeks!). The houses are comparable in size, but the one I viewed today has more potential to add value with a garage conversion and changing conservatory to orangery. Both are 4 bed extended semi detached.
But this house is owned by a couple in their late 60s or even 70s, who are downsizing to a bungalow. The house was built late 60s and they have lived there for over 40 years. It is pretty dated in a lot of places, the walls not very smooth, pipes not chased in walls, original woodwork which is rather naff if I'm honest. Basically I'd want to chase in all the radiator pipework that is currently on show, replaster all walls and artex ceilings, rip out all the dated fitted wardrobes in 4 bedtooms, replace all skirting and doors, redecorate and new flooring throughout. I don't have very expensive tastes, so I can estimate the flooring costs to around 3-4k. But the rest I'm unsure of. Can anyone give me any realistic ideas? I'm in NW england and have attached the floor plan. I have a budget of around 13k.

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Do you intend to do any/all of this yourself? That makes a massive difference, especially to fiddly jobs like skirtings and decrating, where the materials are fairly cheap, but lots of labour is involved.
Replastering would depend on whether you planned to start from scratch (which would allow you to batten out and dryline properly and get lots of insulation in but would cost a lot of money) or just skimming existing plaster.

I would definitely advise decorating and doing skirting yourself - it's very easy to learn via YouTube videos. Easy to do on a weekend without that much effort and would save £££.

What about wiring and sockets? Worth doing at the same time to make it safe.

Any painting can be done by me. Not wallpapering, although with newly plastered walls, I wouldn't want to paper. I wouldn't do any of the other jobs either.
Walls - skimmed I think. They aren't horrendous, but definitely need doing.
I think electrics are okay, looks like they have been done since the house was built. How would I know if they needed doing? And at what cost?

A survey would tell you about age of electrics and recommend replacement with asap, in the future or fine for the time being. You can get an idea from the state of the fuse box. Any smoke alarms should have installation date on them if they're wired in. We're renovating a house in similar state now (possibly bigger - couldn't see the metreage on your pic) and rewiring is about £10k.

We're looking at a cost of £13k for flooring, although some of that is Amtico so more expensive.

We've got a price estimate of £80 each replacement internal door.

We’ve been quoted £3.5k to fully plaster (ceilings & walls) a 3 bed semi about 100m squared after a rewire. Most of the walls are thick with layers of wallpaper so it’s a big job! You might want to test your ceilings if they’re artex as they could be asbestos, fine if you’re skimming over the top but difficult to remove.

Our rewire is quoted at £4.5k, we’ve got quite a few single sockets without switches and reusable fuses in the box so it’s essential.

We’re also having a new roof and heating system done for us and then doing all the other work ourselves (with some help from my brother!). The house needs a new bathroom, kitchen, repainting, etc but we’re going to restore and use the existing skirtings, doors, etc. Our original budget was £15k then £25k when our survey came back and now we think we’ll be lucky to come in under 35k 😭the price of materials, labour, etc is soaring and we’ve budgeted 10% extra for surprises.

I got a laugh reading that one. Took us a day and a half to do the skirtings in one room this week. But to be fair, they're very tall, annoyingly, a bit too tall for my mitre cutter, so we found they had to be started in it, then finished by hand- took a while to work out how to best do it. Also, I'm extremely fussy about things being straight, the walls are not flat or the corners square, and the skirtings have to be removable for when we lay a parquet floor (in a couple of years' time, probably) so had to be screwed in not glued or nailed, so that's an SDS + rawlplugs on one of the lime plaster/brick walls, though we got away with just screws on the plasterboard ones. There is always a snag somewhere..............😝