Car starts first time leave to idle for 30 to 40 mins hit accelarator car cuts out

the car ran fine drive and flew through its last mot no cautions but has strange fault just cuts out without warning at idle and i suspect its the lift pump would help if any one could advise me never had a citroen or puegot before i believe there the same spec... getting a diag too cheers E-Bay lol......just want this to be running as she former was.... if any one has had this fault can you suggest source of problem