I did exactly the same thing for a small office 6ft x 8ft. I had little regards for any building rules or regs, so this is purely what I did and how I did it, whether its "proper" or not isn't for me to say. Make your own judgement.
Sheet of damp proof plastic on concrete floor and I took this a foot or so up the existing brick walls, and left it well over size where the 2 new walls would be.
Timber frame floor sat on top (means a step up, but you need to insulate). I didn't bother fixing this down as the walls tied it in place once built.
Timber fixed vertically to brickwork using frame fixings on existing 2 walls. This was with the thin edge against the brickwork to allow for some deep insulation. I used 150mm frame fixings and countersunk them into the timber by about 60mm.
2x stud walls fixed to floor frame one with a standard door frame, and internal door (with draught excluder and a good fit)
I already had the makings of a loft in the garage, so just insulated and plaster boarded the underside of that.
Floor, walls, ceiling were all stuffed full of fibreglass loft insulation (cheap) before plaster boarding, and chipboard (floor)
Externally I clad it in marine ply, pva'd it and painted it. I then folded the oversize damproof mebrane from the start up the walls by a good 6inces and stapled it neatly in place.
All timber used was bog standard CLS (the larger size 140ish x 45ish) available off the shelf in DIY stores, and cheap as chips. (cheaper still from a wood yard)
2 computers running 24x7 kept it warm for most of the year, on exceptionally cold days I had an oil rad wth a thermostat. I also replaced the old single glazed window with a 2nd hand one of the correct dimensions from fleabay.
Never had a problem with damp (It was full of IT kit). Its been there 4years, and aside from now being home to a multigym instead of office its as it was when I built it. Decorated and carpeted just like a room in the house. Did the bulk of it in a long weekend.
