The Independent (p4) reports that Mr Dugdale immediately took his annual leave but has not resigned from the civil service.
Mr Prescott is said to have been privately critical of the way his press has been handled after a series of attacks on his failure to deliver on the integrated transport strategy.
He is said to have complained that the press campaign about his department's achievements has not been proactive enough and the fightback strategy over negative reports was weak and late.
But colleagues of Mr Dugdale say he has been victimised and is the fallguy for recent bad press. His deputy, Derek Plews, said: 'Simon Dugdale just decided to step down. He has been a head of communication in government departments for 10 years and he decided that was long enough.'