Hi Mulley,
It sounds just like a battery that down on power or is giving up !
But also take a read thro' these two thread for some extra ideas/solution in case its not
LINK #1
or maybe a Relay conversion could be on the cards
LINK #2
If you do get it running by just a battery swap/jump leads after running it say 5 to 10 mins check the voltage output from the alternator with a volt meter (With the engine running, if you can borrow a meter from someone or buy a cheap from Maplins or a similar shop) to see if your getting approx. 13.8 volts at the battery terminal connections and also just check the voltage when the battery's under load with all the lights including the main-beam on , heater blower on max. also the heated rear window and hazard lights on (also check the red dash charging lamp is not on or slightly glowing).
If your still getting approx. 13.8 volts and no red dash light indications the alternator is fine its just the battery needing a good charge if you've not been using it as much whilst you had the Gti on the road recently (Unless the battery's had it's day ) ?
Take it to Halfords for a free check once its been fully charged up to be 100% sure.
I hope this is of help and the info in the one of the threads should sort out your starting problem/s once checked out if it's not just the battery.
If you cannot get hold of a cheap AVO meter PM me so I could arrange something to help out !