So the bushes on the rear anti roll bar were an advisory on the MOT, I have decided to do a 'proper job' and replace the links too as they looked a little worse for wear. I really wish I didn't bother.

For the life of me I cant get the ball joint links off. The ball joint that goes through the bracket on the axle.
I managed to get the nuts most of the way off but then the ball joint started turning and even with mole grips extremely tightly on the ball joint they still spin.

I made things worse as well. I had the bright (read: stupid) idea to cut through one of the ball joint arm, I cant get the grinder in on the nut, so I cut the other side. It was only after I cut it off did I realize that it still wont tap out as the shaft is tapered.

Does anybody have any bright ideas?

I have tried the obvious violence, heat, nut splitter and grinder. But none of it worked and there is not enough room for a grinder or nut spliter.

I dont desperately want to start buying tools, but I do have a electric jigsaw with some blades that the box says will cut through metal. I am wondering if that might be small enough to get into the space.

As you said the top link is tapered and a sharp whack with a hammer should remove it. Don't know why it's being that stubborn.

tighten the nut back up and clean or cut off the rusty damaged threads then undo again