The first thing your mechanic should do is to attach a fuel pressure guage to the fuel rail and test the fuel pressure. That will confirm if your fuel pump or FPR is faulty
it is extremely unlikely to be the fuel pump. Its the first thing that mechanics assume is wrong because a). they do not understand how a complex Bosch fuel injection and engine mangement sytstem works and b). a fuel pump is easy to fit and nets them a tidy sum with no losses. If it doesn't cure the problem they will then say that it was probably a combination of things and offer to replace the fuel filter then the distributor cap and then the plugs etc until hopefully it starts but not before you've spent £500+ [

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As Paul says it is most likely the FPR (fuel pressure relief valve) . This is a valve on your fuel rail which releases excess fuel pressure by allowing some fuel back to the fuel tank. It is doing this continuously to maintain about 3 Bar pressure with engine running. If the fuel system is not maintained at sufficient pressure your fuel injectors will not work. ie no fuel delivery .
The other possibility is that the cold start injector isn't supplying fuel . Either sticky / blocked injector or as others have said the engine temperature sensor which controls the cold start injector.
Also if the FPR is allowing the fuel pressure to get too high the ECU will shut down the injectors. An easy way to check this is to remove one of the electrical connectors to one of the injectors and try start the car. if it starts then that is the problem right there, too much fuel pressure.
(Too much fuel can also be caused by a leaky cold start injector )
One last suggestion is insufficient head of fuel in the tank. If your car has two pumps then the immersed pump assists the external fuel pump to raise fuel pressure . If the fuel tank is allowed to run nearly empty it can either stop the immersed pump working which will then reduce the efficiency of the external fuel pump or running the tank empty can introduce air into the fuel system preventing the fuel pump working properly.
There are some very simple tests you can do yourself with our help before you give the car to a local indie.
Please confirm
1. how much fuel in tank ?
2. have you recently refueled ?
3 have you recently had any work done on the car at all ?
4 do you have an immobiliser.