Just had a similar experience on my 10 year young, 43k Mk2. Similar symptoms, except mine also cut out the the dashboard read out. A workaround was to slap the seat like it was Rebecca and it would crank over.
Problem seems to have originated from water ingress into the starter solenoid/relay housing...the clue was the crusty terminals.
Just waiting for the replacement relay and fingers crossed.
PS - OEM part £98. Ebay option £19.