Labour deputy leadership contender Lucy Powell, who was fired by Sir Keir Starmer in his cabinet reshuffle, has criticised “unforced errors” by the government over welfare.

In her first broadcast interview since being sacked, she told the BBC’s Nick Robinson attempts to cut disability benefits and winter fuel payments had left voters questioning “whose side we are on”.

She urged the party’s leaders to be clearer about their desire to scrap the two-child benefit cap, and move out of a “defensive crouch” on the issue.

And she hit back at claims her deputy leadership bid was a “proxy” for a leadership bid by Manchester Mayor Andy Burnham or Energy Secretary Ed Miliband.

Powell is running against former cabinet colleague Bridget Phillipson, the education secretary, in the contest to replace Angela Rayner as Labour’s deputy leader.

She dismissed speculation that she was seeking to pave the way for a leadership bid by her long-time ally Andy Burnham as a “classic Westminster bubble obsession”.

The Manchester Central MP praised Burnham as a “great politician” and communicator but said it was “sexist” and “wrong” to suggest Labour members might voter for her to be deputy leader to signal they wanted him to replace Sir Keir Starmer as prime minister.

“You’ve got two strong women standing in a in an open and transparent contest,” said the Manchester Central MP.

“And instead of talking about the two strong women, everybody’s talking about this being a sort of proxy for war between two men, which quite honestly, I find kind of sexist, but it’s also completely wrong.”

The Manchester Mayor can not stand to be Labour leader because he is not an MP, but there has been speculation he could seek to return to Westminster in a by-election.

Nick Robinson also suggested Powell could be acting as a proxy for Ed Miliband, who led Labour to defeat in the 2015 general election, if he decided to stand for the leadership again.

Powell, who is Miliband’s former chief staff, told Robinson: “Anyone who knows me knows I’m not a proxy for anybody. I’m me.

“I’m a very independent, strong-minded, effective politician in my own right.”

She said she may have been sacked as Commons leader in Sir Keir’s reshuffle for telling the Labour leadership things “they didn’t want to hear” such as how deeply MPs opposed welfare cuts.

If she were elected deputy leader she said she would be a “conduit” for the views of members and tell Sir Keir “when we’re getting things wrong”.

Speaking to the Political Thinking with Nick Robinson podcast, she said she did not want not want a cabinet job if she succeeds, adding that Sir Keir had been “really clear” that David Lammy would be Rayner’s replacement as deputy PM.

As a “full-time deputy leader”, she said she would aim to bridge the gap between party members and the leadership.

Launching her bid for the deputy leadership, Phillipson has urged Labour to remain united to win a second term in government.

“I won’t pretend this government hasn’t made mistakes – I’ve been first to admit it” she told supporters in her Sunderland constituency.

“But we can’t afford to look inwards – to go back to bad old days of divided Labour Party and open old wounds.

“If we turn against each other only one person will win – Nigel Farage – but millions more will lose.”