I have a 2 bed Victorian terrace; what is the best way to soundproof the walls, that doesn't take up too much space and isn't too expensive

Yup, agree with the other suggestions on here. Batton the walls with some cls timber,couple of 12.5mm thick Gyproc Soundbloc plasterboards screwed together (maybe even more if you want depends on how much room space you can afford to lose,the more the better) but i would also fill the voids between the timber with the board as well. Use any offcuts from other boards to do this as often as you can to cut down on costs for extra boards,and is of course a great way to use any offcuts/waste. If you use 1" thick timber directly fixed to the walls,you will be able to get 2 layers of board between the timbers which will in effect give you 4 layers of soundbloc if you use 2 boards screwed to the timber. Please note though that this may not give you 100% soundproofing as sound can travel through ceilings/floors etc...but will certainly go some way to quieten things down a bit. Hope this has been of help to you. Carl.

build a wooden frame (cls) about a inch away from the orginal walls and fix two layers of soundbloc (looks like plasterboard) on the secound layer cover the first layers joins. roy

Fix resilient bar to the existing walls and then fix 2 layers of sound proof plasterboard. The whole think will be 50 mm thick so you will not loose a lot of space.

I agree with north view. There needs to be a void between the new and existing walls. Sound will travel through solid objects so if you fix battens onto the wall the vibrations will travel through it. Only thing I would add is sealing around the edges.