Off the top of my head , when ever I think of low fuel pressure , first thing that comes to mind would be a weak or failing fuel pump , but before you go out and buy a new fuel pump , replace the fuel filter and the sensor (or see if you can get a good working sensor to test with before buying it).
BMW never changes the filter , on my E46 , I did 200 000kms on the original filter , not realizing it had never been changed , a new filter made a world of difference to how the car performed . The old filter was made in 2002 and was original , it looked clean but there was dirt in it .
So change the filter first , if that fails , it can be a dirty line or your fuel pump . If there's dirt in the line then the tank must have some dirt in it as well but that's kind of a big job to clean and flush the tank i think as so many parts have to come off . When you remove the pump look inside and see if its clean or if there are sediments at the bottom of the tank. If it looks clean then its unlikely that the line is clogged or dirty.
This is my opinion though . Start with the filter , then the fuel pump itself . But in all honesty , I think its the High pressure fuel pump that's going and you should replace that . low pressure fuel pump to my understanding is sort of like a feeder pump that operates at low pressure , High pressure pump is your main fuel pump , I think the newer cars have only one fuel pump , My E46 has only one pump in the tank under the seat , the E30 has two , I have no idea how many pumps our new F30 has but I think yours has one under the seat as well .
If the fuel filter helped and corrected the problem , then I would also plan on replacing the pump as I feel a clogged filter would probably put extra pressure on the pump making it work harder which would lead to premature wear (someone can correct me on this )
Also if you fit a new pump , don't let the petrol in the car go very low , the Pump needs petrol to keep it cool and when the petrol is low , the pump heats up and if you do it to often this can also lead to premature failure .