City have released longest-serving player Lee Bullock, as well as Marcel Seip and Rob Kozluk.
Phil Parkinson will also be hoping that David Syers reconsiders and signs the deal he turned down in January.
Parkinson wants to shift those on the fringes of the squad. Midfielder Luke Dean, who has hardly featured since turning pro, has also gone.
Branston and Williams are among six still in contract who are no longer in Parkinson’s plans.
Nothing has been said about keeper Matt Duke but Northampton are thought to be considering a permanent move after his fine form there on loan. City are unlikely to stand in the way of any offers.
And Mark Stewart, who went back to Scotland on loan at Hamilton, is close to agreeing a settlement to leave the club.
Bullock made 129 appearances after arriving from Hartlepool on New Year’s Day 2008, helping Stuart McCall’s side to a 2-0 win at Accrington on his debut.
The no-frills midfielder became Mr Versatile with roles as a holding player, a centre half and even a target man on a couple of occasions.
Named club captain by Peter Taylor, he was one of the most popular members of the dressing room.
His departure, following on the heels of Michael Flynn and Craig Fagan, clears room in the budget for Parkinson to freshen up his squad for next season.
Full back Kozluk was brought in as a stop-gap in January when Ramsden was injured but finished on the left.
Dutchman Seip filled in well across the back four before a shoulder operation curtailed his campaign. But with his family based in Plymouth and a baby due next month, he was not pushing for a move north.
Meanwhile, Matt Fry is set to be invited back for pre-season to prove his fitness before the club make a decision.
The young left back had been carrying a groin injury since arriving at Valley Parade in January and recently underwent surgery.