Running Rich

[Simong]

Hi all, reaching out for a bit of help if possible.
I am fairly experienced mechanically but am a bit stumped with a fault I am getting.
2.0tsi engine runs fine ish from cold…but on hot restarts struggles sometimes to fire unless throttle pressed. Or just runs quite choked.
Data suggests that the lambda often rails at -25% furling and the spark plugs are sooty thus suggesting running very rich. Sometimes triggers a Rich fault code. I get the overrun popping when it’s in this mode. Motorway or ‘steady’ driving seems fine. Fuel pressure doesn’t seem to decay on switch off, so don’t think it’s leaky injectors.
I have a new hpfp to fit as I thought it could be leaking past seal. But oil seems ok…
Any help gratefully received

[Simong]

For information this was indeed resolved by fitting a new high pressure fuel pump.