So, the only issue found by my mechanic in the post sale inspection that would lead to an MOT fail was a split gaiter (rubber boot) around one of the ball joints.
The ball joint I needed to replace was here:

It’s held in by four bolts, three on the top which are vertical and one, larger, bolt which is horizontahorizontal:

If anyone with a Tiger Super Six is reading this before setting off on this job you shouldn’t need a ball joint press. I bought one and then found that the ball joint is held in by the three vertical bolts. It isn’t pressed into the upper suspension arm. You will, however, need one of these:

This is a ball joint splitter. The interference fit between the ball joint pin and upright is so tight that you won’t get it out without this and a lump hammer. 3 days of huffing and puffing followed by 45 seconds of gentle tapping! The tool only costs £7!!
I did run into something of a hitch once I offered up the new ball joint. I’m not sure if Tiger drilled the wrong holes (in slightly the wrong place) or if my Tiger has been modified to take M8 bolts (rather than M6s) but the holes in my suspension arm were 2mm bigger than in the new ball joint. I cable tied the ball joint into position and then drilled the holes out:

I’m not sure if this was correct but I did grease the ball joint pin lightly.
Once I’d fitted the joint, I took the car out for a spin. Felt exactly like it did before which is what I was hoping. There was no play in the old ball joint (only the split rubber) so it shouldn’t have felt any different.
I’ve given it a quick coat of black paint to seal it. As you can see from the pictures above the suspension arms do need repainting. I’ll do the ball joint properly when I’ve doing this.
Job done!