Quick update - not that my mystery bug is all but gone, I finally got round to getting the 4 wheel alignment done with a 'fast road' set up.
I could tell that it was out, but it must have been quite out. The fronts in particular had camber and toe issues. To be fair, the garage that did the resto were going to get it done for me, but with the MOT snag, they weren't able to.
It drives like it's on rails now