Can anyone give me advice on replacing an old chipboard floor with new chipboard that goes under partition walls.

Knock the wall down, lift the old chip board, fix the new chipboard then replace the wall - easy !

Serious answer - You need to check if the chipboard is laid up to the wall or extends under the wall.
Remove a skirting board (behind a wardrobe or similar so it doesn't show)to see whats going on.
If it extends under the wall then it's 99% sure bet that the joiners has fastened the wall to the floor through the board and you'll have to cut the board as close to the wall as possible to get it out (be carefull not to cut the joists under the board if using a jigsaw etc).
Whatever you do, don't go ragging it out - you'll split the joins in the plaster board walls and end up with a real mess to sort out.