Mine was £10k for the structure (ie no insulation/floor/p'board or electrics) about 5 years ago but did include a dormer out the back to give an area where you could walk about stood up. Not knowing your precise arrangement, I don't know whether this is what you would need. Mine was half the area of yours and in Oxfordshire. If you do want a dormer and are in London and are twice the size and 5 years later on, Mr McArdle has a bit of a point! If you are intending to make the room "habitable" which, for many authorities means having a fixed staircase, they may insist on a dormer - again, not sure what your design is. For a "properly registered" conversion, as you put it, by which I assume you mean with planning permission and conforming to building regs., there will be knock on costs (fitting of door closers to all doors on escape route, removal of glazed doors opening onto escape route, half-hour fire doors and half-hour fire protection to floor and walls and new joists, which will be an unavoidable part of the cost.
If, on the other hand, you have a non-fixed stair (ie loft ladder) and claim the room is not habitable, you could get a local builder to fit a Velux (or do it yourself) and insulate and wire yourself and assume the ceiling joists will take the weight. Not a good selling point when you want to move however!
Before you ask for detail, do a Google search through the NG archive - the subject has been done to death (several times) already!