I have an 03 plate Punto 1.2 Active.

Occasionally, and more recently, more often, when I switch on the ignition, the fuel pump doesn't prime.
It can work ok 3 or 4 times, but then the next time, nothing.
When it does work, the car runs just fine.

I've checked the fuel pump relay in and out of the car and it works perfectly every time.
I have also checked the power connector to the pump and it;s all nice and clean inside.
I have also reset the inertia switch, just in case.

On the occasions when it doesn't prime, if I apply some "percussive maintenance" to the pump with the rubber handle of a screwdriver, it almost always works when I try it. Then after 3 or 4 more successful attempts, it will not work again.

Does this suggest that the pump works ok (it keeps going once it has started), but sometimes gets stuck?
I guess the solution in that case is a replacement pump
I don't want to go to that expense if it turns out to be something else.

Could it be bad connections somewhere - perhaps on the inertia switch?

car starts even when pump doesnt prime?

When it primes ok, the car starts and runs just fine.

When it doesn't prime, the car starts but stalls after a couple of seconds once the fuel in the line is used up. It won't start again after that, of course, because there's no fuel.

When I can convince the pump to prime, by hitting it, everything is ok again.

then it must be some bad connector/cable at the pump, try finding out which one is it, and then cut it from scrapyard donor car and simply wire it

Ok. Thanks. I did check the connector and it all seemed ok. Very clean and a good fit. Maybe there's a problem somewhere further back in the wiring. I'll investigate a bit more.

If you put positive 12volts on the thick purple and yellow wire and negative on the other thick one (black?) when it does not work and nothing happens then it will be the pump.

It was the fuel pump. It suddenly became really noisy when it was working.
Couldn't afford to be without it for too long, so managed to get my local garage to replace it the same day. £110 for the part, plus an hour's labour. Now I can't even hear the pump priming except at really quiet times.

Thanks for everyones' suggestions though.

BTW. Anyone in the Bournemouth area - I recommend the garage Targa Florio on Christchurch Road, Boscombe, who fitted my car in between other jobs and had it back to me the same day.