car is cutting out?

Try if not already done diagnostic unit at Peugeot garage. Cost but worth finding out the exact problem as it could be any one of a number of faults.

Quoting Model and fuel type helps too when submitting a question..
Guessing all, fuel injector failing, low compression on cylinders.fuel filter dirty, fuel pump fails in higher revs under load.
One more guess, in this happen on one of my Ford cars, fuel tank caps have air hole to prevent a vacuum which would stop fuel delivery. Get your mechanic to try short run with cap off, not his/her's< (not sexist) the tanks filler cap.

Bob uk
March 2016