Depends enormously on how easy the access is and whether the stucture would need much changing. Ours (only half the loft converted, creating one new bedroom, no ensuite, with a dormer and 2 velux windows) is iro £50k, but there was a big steel that had to be removed first, so it wasn't the easiest of conversions.
Very unlikely that you'd get a builder to let you pay on finance, but you may be able to extend your mortgage to cover it.
Agree with MP that I can't see any way to get change from £10k, but likely quite a bit more.
We've just had one completed last month. We had a 'proper' staircase to match our existing one built which leads up to a study area (was going to be a separate study room but at the last minute we decided to have it open plan with a bannister type railing to give more light down the stairs) and then a decent size double bedroom. 3 x velux windows, 2 in bedroom and 1 in study area. No en-suite. was quite a major job, they started 1st week in July and finished end of August and had to move and box in the water tank. Cost of loft converstion itself was around £25k (including carpenters, plumber, electrician and plasterer) but then we had to get it decorated which was another £1,500 and carpeted, (£1,300) Was definitely worth it though as the whole lot was less than the stamp duty if we'd moved to a bigger house. we used a company called Econoloft who are based in Lancashire but have a London office too.