He was speaking after Mr Sunak said people would receive the £600 payment this winter and an announcement would be made soon.
Winter officially starts next Wednesday, December 21 and runs until Monday, March 20, 2023.
Mr Eastwood said people need clarity, not more broken promises from a Tory government that has failed to deliver during the cost of living emergency.
Said the Foyle MP: “Families in the North are fed up with being messed around when it comes to the £600 energy support payment that they desperately need.
“Since this payment was first mooted we have had various dates bandied about and multiple broken promises from the DUP and the British government on when people could expect it, what we need now is absolute clarity on when this money will be paid to people here.
“Today’s announcement from the Prime Minister will raise the hopes of many people across the North who have already waited far too long for this payment.
“Many are struggling to afford presents to put under the Christmas tree, the elderly are being forced to ration heat in their homes and parents are skipping meals so that their children can eat.
“Talk is cheap.
“We can have no more false dawns and we need the PM to get on with delivering this money to those who need it,” added Mr Eastwood.