How can I fix starting problems with my Citreon Saxo?

I have an S reg Citreon Saxo which starts first turn of the key in the mornings and most other times except A) if you only travel about a mile, stop and then try to start again it just will not go - I can go a bit further and not have any problems B) Last night I got home at 5.45 and went out again at 6.15 and it would not go. Leave it for a while and it goes or sometimes if you keep the key turning it will eventually fire up. A couple of mechanics have looked at it but can offer no answer. Has anybody else had this problem. Also the engine revs itself (the pedal goes down and then back up which can be embrassing sat at traffic lights as there is nothing I can do to stop it - we had the accelerator cable replaced as it was kinked but it is doing it again.