In Peterborough the places that I tend to go to are:
Charters (Boat on the river)
Brewery Tap (in town but away from all the main pubs, so don’t get any idiots in there)
Palmerston Arms (nice pub that just serves real ales, though have introduced Becks on tap recently)
Cherry Tree (nice pub, been in there a few times, first time was when Everton played Posh in the Carling Cup a few seasons ago)
Out of those four pubs, the Palmerston Arms is the only one that does not do food. All serve real ales as well as normal beers/lagers. During the week none of them will be too busy.
Hope that helps mate, any other questions just shout.