Burnham was officially declared as the new Labour Party leader on Friday following a short contest in which he was the only candidate, having secured the backing of 379 MPs.
Some opposition parties have urged Burnham to call a general election in order to ensure he has a mandate for his premiership.
However, Powell insisted Burnham would stick to the promises made in Labour’s manifesto in the 2024 general election.
“Our manifesto did talk about the redistribution of power, it did talk about the rewiring of our country, it did talk about taking on some of those vested interests,” she said.
“He [Burnham] really understands the bigger, bolder measures that are needed to live up to the manifesto promises.”
She also said his leadership was a chance to “reset” and that scrapping the Digital ID scheme was a “small example of reprioritising”.
In one of his first announcements since becoming Labour leader, Burnham said he would ditch the plan announced by Sir Keir last year.
Powell said the scheme would have cost a “not insignificant amount of money” but would also have diverted attention from the government’s priorities.
Separately, the BBC has been told Burnham’s government will announce plans for new oil and gas drilling in the North Sea.
Powell said Burnham would be “pragmatic” on the subject, adding: “I don’t think it’s a change of policy. It’s more a change of emphasis.”
The announcement is expected to be part of a package of measures including plans to take water and energy companies under public control and a new council house-building programme.
Burnham has previously said he wants to see “greater public control” of the water and energy sectors and has called for Thames Water to be nationalised.
In her interview with the BBC, Powell also backed increased public ownership, arguing the economy had been “overly privatised” and the “utilities and essentials of life don’t work in the interest of ordinary people”.
She said bills were “going up and up because they are run in the interests of private interest, not for the consumers or for taxpayers”.
But, speaking to the same programme, former Conservative minister Jacob Rees-Mogg said: “The water industry needs private capital or it has to have taxpayers’ money – no other money is available.”
