Quite a few threads on TD5 starting on here and elsewhere a bit tedious to read them all, but would pay you to learn what works and what doesn't work.
Seems to me having been through the mill with my TD5 one of the big issues is gasses in the fuel feed to the head, and the copper injector washers are prime culprit they allow combustion gass to blast past and into the fuel system, the bleed valve deals with this ok for a while but it gets made up with muck and gives up, pressure regulator on the back L hand side of the head can be a problem look for any diesel running down the back of the engine and over the starter motor, they are pretty cheap (use a repair kit not the whole unit) and not too hard to change.
I took off the filter housing and gave it a good fetteling then re sealed all four connections with new copper washers changing the bleed valve at the same time, this seemed to help loads.
Take care before you go ahead and change the pump, seen loads of posts where they change it and find it's just the same, not saying it's 100% that this is not the problem but try and check. Pressure at the regulator should be maintained at 4 bar if it falls away when the engine is pulling and consuming more fuel then could be the pump, but it may be that this is when the injector washers are allowing gas to blow through into the fuel rail and the injectors can't fuel correctly.
One other thing is the fuel filter, it has a seal in the centre which can get left on the centre stem, when you put a new filter in place complete with seal then you have two seals on the stem, and it causes a sealing problem.
Most of all good luck and let us know how things go.