Thanks Tabetha!

I opened up the starter, rubbed down the ends of the brushes with fine paper, they were pretty black at the ends but nowhere near fully worn, also rubbed down the copper shaft which was quite black. I cut off the crappy connection on the end of the solenoid lead, and crimped on a proper ring connector, with nut and washer securing it, just like the main power lead.

Fired it up, sorted! The motor fires up every time as good as gold.