Fuel pump or something else....

[Wazzzer]

your cat won't last long if your pre cat lambda is dead...

[Rhyso]

Engine speed sensor is the crank sensor if im right. They can deteriorate because of the heat from the engine.

That's the one mate, its to the side of the oil filter on the block,. Its all fitted now so I'll have to see how I get on 

Sounds like you've found the cause. Classic symptoms if once warm the car refuses to restart until the sensor has cooled down