Had the same issue with my fuel pump on my 2.5 Rover 75.
The local car service guy got it going by banging the fuel tank with a rubber mallet.Had to replace the whole pump as the mechanic reckoned when they tried to start it again it up again the pump wouldn't work unless they tapped it.
Reckons the bushes were worn and that part is sealed so replacement required.

How did the garage know the brushes were worn when the unit is sealed? Petrol pumps are a cash cow for many garages. Few petrol pumps actually require replacement. Fixing FFS correctly is not a very lucrative job. Replacing the pump at the same time is. Your pump may have failed, they will eventually I guess. It's the first on the Forum.

TC