I would agree, you could try hitting the starter with a hammer as they can sometimes stick.

Eee, 'eck. When I were a lad... If our Minis went for 100,000 miles before they rotted away, they would have had at at least one re-built alternator, if not two, and the starter motor would have had to be removed and a new Bendix gear fitted (I've got one on the bench in front of me if anyone wants it). My present car has done 166,000 miles in six years and it's still got the original alternator and starter motor. If the starter motor lasts as long as yours has I will be very happy. Parts are - for most cars - so much better made and so much more long-lasting these days. As Collosus and Peter say, it's probably just the Bendix sticking, after thirteen years!