Fuel pump

Can anyone tell me what is pushing the manual fuel pump lever up and down to pump fuel ? I have my series 3 2/4 in a garage at the moment they are saying lack of fuel ? I have put a new fuel pump in I do know there is a certain p.s.i range for the fuel the garage it is in dies have a very good reputation but concerned with classics as most of the vehicles they do are modern prices of crap with 100 sensors that are not needed . Also the coil is extremely hot as the engine kept cutting out can anyone recommend a high quality coil not worried about expense just need it to run properly many thanks all