Some years ago mine used to do this. It used to start eventually mind, but would take an age to do so.
It went away and I think the only thing that happened in the mean time was a service, so possibly the fuel filter?
There's a possibility that it's unrelated but the fuel filter is easy and cheap enough to change if it hasn't been done for a while. Might as well give it a service...
I'm pretty sure nothing else was done between symptom and solution. It's worth noting I didn't go looking to fix it, so whatever fixed it was routine....