The Greater Manchester mayor said he supports workers doing what they need to do to protect their incomes during a cost-of-living crisis.
Responding to questions on his own future, Mr Burnham insisted he does not expect there to be a vacancy to replace Labour leader Sir Keir Starmer and he intends to serve a “full second term” as Greater Manchester’s mayor.
Durham Constabulary are looking into whether lockdown rules were violated after Sir Keir was caught on camera drinking a beer in an MP’s office after a day of campaigning for the local elections in Durham in April 2021.
Sir Keir has said he will stand down if he is issued with a fixed-penalty notice.
He has also come under pressure from unions to stand up for workers’ rights and support recent industrial action.
About 40,000 RMT members at Network Rail and 13 train operators went on strike last month in a dispute over jobs, pay and conditions, and further action could follow.
Holidaymakers also face chaos at airports this summer as BA staff demand the 10% of pay they had “stolen” from them last year as they faced “fire and rehire” tactics.
Mr Burnham, speaking to the BBC’s Sunday Morning programme, said the Government should “stop demonising” workers who are fighting to protect their incomes, themselves and families from a cost-of-living “crisis”.
He said: “Nobody in my position should ever, in my view, criticise people for trying to protect their incomes in a cost-of-living crisis, that is absolutely what they should be able to do.
“They would say, the unions say themselves, that nobody wants to see strikes, but when you’re faced with a Government that is sitting on its hands and doing nothing then strikes become inevitable, and I’m putting to you we don’t want to see that, it requires people getting around the table and sorting this out.”
Pressed if he supported striking rail workers and BA ground staff threatening to strike, Mr Burnham said: “I support the rail workers, I support the BA staff, in that they have got to do what they need to do to protect their incomes.”
Asked if he would go on a picket line, Mr Burnham said: “I have done, in Greater Manchester, where there were bus workers being victimised with relation to what people call fire and rehire.
“You’ve got to judge these situations, haven’t you, as to what extent there is a principle at stake and where there’s a principle at stake I have no problem in showing that support.”
Asked if this meant Sir Keir was wrong to say going on a picket line did not show leadership, Mr Burnham replied: “I’m not saying that at all, the leader of the Labour Party is in a different position from me, I’m not saying I’m in the same position.
“There is a balance to be struck always between supporting workers but also helping the public go about their business.
“What I am saying to you today is the Conservatives are more interested in laying a trap for the Labour leader rather than sorting the issue out.”
On whether he would seek to replace Sir Keir as leader, Mr Burnham said: “Firstly, I can’t because the rules don’t allow it, I’m not a member of the parliamentary Labour party.
“But secondly, there isn’t a vacancy and I don’t expect there to be one.
“The only reason I’m coming on this programme this morning is to support the leader, to support the Labour Party in taking the fight to the Government.”