It could be any number of things. First step is to get the fault codes read. If it's P1211 and P0251 it's time to start praying. If the fault code is P0340 then it's the cam sensor - It happened to mine last week while overtaking. A £25 sensor and two mins to swap and it's fixed. If your sensor is black, then it's an old one, which are renowned for being a bit dicky, new ones are grey, and better.

It 'could' be any number of things including the injectors, pump, cam/crank sensors. It's a very hard thing to accurately diagnose, as the fault codes aren't very specific. One thing to investigate (if it is P1211/0251) is the Inlet Metering Valve which is mounted to the pump, and can cause the symptoms you mention, but is a lot cheaper than swapping in a new pump.

It could still be injectors, as they can be fucked and the car can still start fine, and not smoke, but it's unlikely with the cutting out.

Get the fault codes and take it from there. PM me if you get the codes and want more info.