Painting over wallpaper is a chancy business. You should do a test patch 1st. Much better to strip it off and line the wall. The joy of this is that you need not be a too clever paper hanger, because you can fill MINOR gaps in the lengths with filler before painting. Also, even tho you should prepare the wall first, you get a second bite of the cherry with lining. You can fill or remove missed irregularities prior to painting.
Apply 2 or more coats of paint. Even amateurs should get a very good finish, and if you have let the paper dry thoroughly before painting, no bubbles should appear.
This treatment will serve as a good base for repainting for years and if you tire of a paint finish, prepare 1st then conventionally wallpaper on top.
reception, you have little choice but to have the carpet laid (it sounds like its imminent) then do as chazza says, and here, using plenty of dust sheets to protect the carpet. Your �150 charge isn't excessive these days, and it's a lesson learned.