Intermitent starting problem

If I've been stationary for a long time the car will start no problem and will run well until I stop. If I try to start the engine again after a short stop the engine sometimes doesn't start first time. I have to wait 5 mins and then usually it will start. If after starting it I can run it at an even speed it's fine but if I have to crawl in traffic or stop at lights it dies and then won't immediately start again.
The red lights on the dash come on and the fuel indicator shoots up really quickly.

I had a guy come and look at it, his machine didn't detect a fault but he thought it could be the alternator? Any ideas would be great as I don't want to have to pay a lot of money and the problem not fixed?