New ≠ fixed. Follow the symptoms. You need to check gas pressure after the engine is off.

Also when running: pressure should be rock steady; when my wife's E53 had these symptoms, including the last hard start of taking about 8 cranks of 8 seconds, the dial jiggled with every injector pulse.

Also: people think that the FPR's job is keeping pressure stable, the main job is to hide the symptoms of a failing electric pump.

Ends of life pump (about 5000 hours average), they get weak and won't produce enough pressure to make the extra to also run the siphon jet.

Not having the regulator on the rail saves pumping all the fuel to the rail and picking up engine heat. The processors got fast enough that they can keep up without the manifold vacuum compensation so that was another reason the regulator doesn't need to be on the rail although BMW left the vacuum line in all the way to the engine bay anyway as a vent.
Filters clog depending on how much dirt they are filtering.

It's still playing up, I'll change fuel pump tomorrow, fingers crossed that fixes it!

Yep and the insanely large filter on e53 can easily last half a million miles. You'd have to be in an exceptionally bad area to get enough dirt in your fuel to ever plug that filter. At 180,000 miles I cut mine in half to inspect it was maybe 1/3 consumed.

The tank had less than a gram of dirt at the bottom after ≈ 2 decades. In the USA at least it's pretty uncommon to get dirty gas from mainline stations though I did see a guy posted recently he had a rust issue so a solid preventive measure he took was a magnet glued to the bottom of his tank near the pump foot.

Fitted new pump today, seems to have fixed the hotstart issue. Happy days! Cheers guys

I would still follow up with pressure leak down lest you get caught with a no-start situation due to leaky FPR but awesome on fix helping!

Fpr is new with the new fuel filter. I do have what sounds like a fuel pump whine, is there more than one?

Pumps whine some louder than others. I can usually hear when engine isn't running but not in the car when it's not.

Okay, so don't worry about that then?

Not unless you can hear it in the car while running.