That is correct.I paid £75 last time I got a thread cut but that was not proofed. It was going to be £150 proofed.
You don't have to have your rifle proofed but if you want to sell it on then it is a legal requirement, or so I'm told.
Cheshire gun room......£35........doesn't need reproofing (cant remember the name of the expert opinion, I'm sure someone will though)
Despite the proof houses trying to put the myth about, it is NOT necessary to get a barrel re-proofed after threading. To require a reproof, you would have to do something that "significantly weakened" a load bearing part. Now, firstly the muzzle takes very little load, and for very short amounts of time. The pressure at the muzzle is tiny. Secondly cutting the thread doesn't significantly weaken it. It could be argued in fact that the addition of a moderator strengthens the muzzle.