I think James it right re the relay because I had exactly the same problem with a MkIII Golf many years ago. The engine would die, but you could hear the fuel pump when trying to restart. After taking it to a number of specialists, one of which replaced the fuel pump, and disconnecting the immobiliser it was still happening. I joined the AA as a last resort and when it broke down, luckily for me the guy knew exactly what it was; a faulty relay. He popped the cover off and wrapped an elastic band around it and it fired up straight away. I think the relay was only about £10 from VW in the end too.