You would need to check that there isn't a condition set by the council that you can't convert it. They can be removed but usually depend on the off road parking set up.
I converted a double garage, and changed the doors to windows, so for a double it was around £11k. But for a single you can go as little as £6k but up to £8k. For a bedroom you need to concentrate on insulation.
If the garage is fully integral ie is the same width as the house then it would be double walled with a cavity, where you need to pay close attention is where the garage sticks out from the house so it would have a single skin (brick wall no breeze block internal wall)
If you retained the front garage door and used the space at the front for storage, ie when the garage door is opened (if it is an up and over door or pivot style door) you can build a wall just behind where the door extends and this should be cheaper.
Windows wise it would depend if there was one already and if you could put one on the side wall.
I was lucky that a builder could give me a ball park figure before I even bought a house, he said to budget £8k. I am in Yorkshire, I hope this helps give you a general idea.