Update: battery was off for 2 weeks. Auto electrician removed the battery (to retrieve the 10mm spanner I had dropped in when disconnecting!) and found and removed an ancient rusty allen key. So, one more rattle gone - result!
He re-connected the battery. The new relay was still in.
It now starts on the button. 4 times in a row so far - I am trying to re-set the ride height before getting the toe settings done, so lots of start / stop. I am hoping the guys can at least measure camber and give me a datum point so I can count the shims to adjust ... I don't have Back on Track or similar here to do that.