The figures were uncovered in research conducted by the charity Independent Age, who say that on average, pensioners are potentially missing out on payments of £63.54 each month.
Councillor Sykes said: “Pensioners are already facing severe cost-of-living pressures with energy bills and the cost of the weekly shop rocketing, an extra £60 per month could make a massive difference.
"Oldham Council must play a proactive role in reaching out to and helping these pensioners claim what they are entitled to.”
Independent Age research also shows that 51% of over-65s across the north of England are making considerable cutbacks to save money for energy bills and essentials.
Councillor Sykes added: “The fact that more than half of pensioners are struggling to make ends meet is a damning reflection on this Conservative government.
"They have left people behind to fend for themselves.
"Blame for the cost-of-living crisis lies squarely with the Conservative party.”
