Golf Mk1 fuelpump issue?

Greetings ladies and gentlemen. Was out on a drive yesterday when the wonderful golf randomly started to stutter and then the engine just stalled. Pulled off to the hardshoulder and turned the key, the car start just as easily as before and runs perfect as usual! this issue is only happening in decent high speed (45Mph, 70km/h) Also sometimes if i floor it the stuttering starts. Ive tried adjusting both ignition and the carb but no difference at all. Could it be the fuelpump? anyone had similar problem?    

weber or original 2e2 carb?

A weber 32/34 dmtl, i followed my instincts and replaced the fuel pump. Works good now. Hopefully people with similar problem can learn from this.