Thanks for all the replies.
I should probably have said that I haven't driven the car all that much since I replaced the internals of the solenoid (car was off the road for a number of years during resto).
But even so, you have convinced me that the solenoid seems like the most probable cause of the problem.
And since trying to rebuild the solenoid didn't do the trick I think I will buy a new starter and hope that solves it
