A patrol car was seen on double yellow lines in Clifton last week and a Bristol University car a week later.
Avon and Somerset Police said there was operational activity in the area so officers "could have been" visiting the bakery to advise on security measures.
Bristol University said it had identified the officer responsible who had apologised "unreservedly".
The police car was spotted on Tuesday last week while the university security car was photographed on 24 May. On both occasions uniformed staff were seen in a nearby bakery.
A police spokeswoman said without a number plate or vehicle ID it was "very difficult to trace which officers were involved and what they were doing".
"If the officers were not attending to operational duties and were just there to buy their breakfast then it would not be what we expect from them," she said.
"If they are found to have breached this advice then the matter would be referred to their supervisors."
Bristol University said: "We have identified the officer responsible and reminded her of the university's standard operating procedures. The officer in question apologises unreservedly."
Meanwhile Bristol City Council said it would not be issuing finesas its parking attendants have to witness any wrongdoing first hand.
Police officers and security staff have been spotted parking on double yellow lines outside a bakery in Bristol.