Tilly, thank you.
I would have had plenty of change from your budget.
Labour (rip out, install suite, false ceiling, spotlights, underfloor heating, and tile) was £1500, which included the underfloor heating kit and lights). All done by the one guy. He got an electrician in just to wire up he UF heating controller.
My bath, wc, sink, taps, screen, radiator, came to £650, from Wholesale Domestic and using the plumbers trade discount. Shower was separate, about £120. Shelves, £100ish.
Tiles and grout, £400. I only got the bath and sink area tiled. The remaining walls still need plastered and painted.
So cheap, but cheerful. That’s all I needed for the next couple of years.