Sunak, 43, assembled his new senior ministers for their first meeting at Downing Street on Tuesday morning, describing them as a "strong and united team".
"A warm welcome to those for whom it's their first Cabinet and also a welcome to those for whom it may not be their first time," he said in a nod to Cameron, who sat opposite him at the green Cabinet table.
Sunak's Tories, in power for the last 13 years, including six under Cameron, have been trailing the main opposition Labour party in opinion polls for months now.
The latest Savanta survey published just before Cabinet met put Keir Starmer's Labour 18 points ahead of the Conservatives on 46 percent, and on course to become the largest party in parliament.
Sunak's time is running out to turn around his party's fortunes, which has been hammered by a cost-of-living crisis and repeated scandals.
On Wednesday, the UK Supreme Court judges rule on the legality of the government's proposed scheme to deport some asylum seekers to Rwanda.
Defeat will force ministers to think again on how to control immigration, which has been a key issue since the Brexit vote that Cameron instigated.
Finance minister Jeremy Hunt meanwhile outlines government spending plans next Wednesday, resisting calls from Tories to cut taxes before the election.
Sunak has made stopping the "small boats" crossings of migrants from northern France and driving down inflation key planks of his administration.
He told colleagues he was confident they were making progress on both, as well as getting the economy back on track and cutting hospital waiting lists.
Cameron, now 57, resigned in 2016 immediately after losing the Brexit referendum. Since then, his party has lurched to the right.
Former foreign secretary William Hague said his old boss would add "weight and substance" to Sunak's government after the divisive Brexit years under the populist Boris Johnson and economic turmoil triggered by the short-lived Liz Truss government.
"His (Cameron's) central achievement in 11 years as party leader... was to give the Conservative Party a much broader base," he wrote in The Times.
"Cameron's renewed prominence is a reminder that the cabinet in which he will be sitting is mainstream and centre-right," he added.
Cameron is no longer a sitting MP and has had to be made a life peer in the unelected upper chamber of parliament, the House of Lords, to be able to sit in government.
That has raised questions about accountability in the elected House of Commons.
