Sure, you may have small air gaps from inaccurate cutting and some thermal bridging from the studs, but overall, this method will significantly increase the R-value of the room over what it is now.
As noted in a comment, you could just glue the foam boards on. This would eliminate the thermal bridging concern of studs, but you could still end up with small gaps anywhere you need to cut the rigid foam. You would still need to apply something over the top of the foam boards to
- protect them from damage and
- give a solid surface for attaching anything to the walls.
Whatever you use for this would need to be anchored through the foam and into the masonry wall for stability, bringing back some amount of bridging and possibly leaving unintentional air gaps. This would lead me back to using studs, as they would be the perfect thing to hang that interior finish plasterboard from and they'd give you that solid mount for any wall-mounted furniture and/or decorations.
Any air gaps caused by inaccurate cutting of the foam board to fit between studs can be fixed with low-expansion spray foam to fill the gaps between the foam & studs.
A double-stud wall with offset studs (as is often used when looking for noise isolation) will also break the thermal gap if you're really looking to maximize the insulation. The bigger concern (in my mind) is the reduction in interior floor space, especially if you go with a double-stud wall.
Assuming that "decorated room" is British English for "there are interior finishes on the wall" (American English), well, yes, you'll have to remove those finishes and/or cover them up, depending on the type of finish. If it's just a layer of painted plaster over the masonry exterior wall, I can't see any added value to removing either the paint or plaster. If you've got wall paper, I don't know that attempting to remove it would buy you anything either.
If it's wood paneling/wainscotting or something like that, then you'd probably want to carefully remove it so you can reuse it on the newly build wall (or for some other purpose), instead of leaving it trapped inside the wall forever. I doubt that it would do any harm, though, if it were left in the wall. It would make a nice archeological find for someone in the future who may choose to do a full renovation.