You might be able to do it if
You can reuse the existing carcasses and appliances and just replace doors, plinth, cornice, worktop, sink and taps. You might be £2.5k from Howdens etc . Plus £1k in labour ( mostly joiner ) .
One thing that really makes a kitchen is good lighting and the materials are cheap , it’s just the labour for the electrician.
You can get inexpensive ( but nice tiles ) and don’t tile the full bathroom.
You use small tradespeople who are not VAT registered or someone who will do it for mates rates.
Bathroom stuff doesn’t need to be expensive, as long as you can use the existing layout ( moving plumbing is expensive ) .
I just did up a small bathroom and shower, tray , waste, shower enclosure, WC, WHB , taps and waste, vanity unit, heated towel rail and valves were £1100 ( and that’s with a branded shower tray as the one I wanted was out of stock ).
Tiles were £9 and £10m2 from Wickes. I only tiled 3 walls and floor and painted the 4th . That meant only 14m 2 of tiling and not 20. Also it’s less clinical IMO.
Your problem is going to be flooring as cheap flooring is often a bit rubbish. Also if half your cost is labour it’s a false economy. Could you get something decent for £3k?
So 4k on kitchen, 3k on bathroom and 3k on flooring ? You could put down cheap carpet for a lot less than that, and replace it when your kids have left home. But it will look a bit rubbish in a few years. I’d go for hard flooring myself.
That’s left nothing for decorating so you need to do all that yourself . You’ll be a few hundred for paint - are you just doing the walls or the woodwork and ceilings too? That’s quite a lot of work - it’s mostly prep. Are your walls in good condition ?
And it’s also nothing for contingency - you should ideally have 10%.
Nothing for new furniture. Or strip out and a skip. Nothing for plastering so let’s hope your walls are plaster on brick and not plasterboard.