Andy Burnham will present ministers with a proposed “levelling-up” deal for Greater Manchester when Boris Johnson travels north for the Tory party conference.

The Greater Manchester Mayor said he will seek Government support for a package including the establishment of a London-style public transport system when ministers descend on the city next week.

Meanwhile, London Mayor Sadiq Khan said his city should not be ignored as part of the levelling-up agenda – and warned Labour colleagues against “slagging off” the capital.

At a Labour conference fringe event in Brighton, Mr Burnham said there was “outrageous” inequality between transport costs in the capital and elsewhere.

In Greater Manchester, a single bus fare could cost more than £4 while in London it was £1.55, he said.

“I have taken the decision to bring buses back under public control. That is the precursor to build a London-style public transport system,” Mr Burnham said.

“When the Government comes to Manchester next week I will put on the table a constructive proposal – a levelling-up deal – that has a London-style public transport system at its heart.

“If we had that same level of fairness, I think it would change a huge number of lives in our city region.”

The minister in charge of the Government’s levelling-up agenda is Michael Gove and Mr Burnham joked: “We are very keen to impress the new Communities Secretary so we are going to lay on a special Warehouse Project Hacienda night.”

He said the deal would make political sense for the Government – because Boris Johnson could blame him if it failed and take credit if it succeeded.

“We will build a London-style public transport system by 2024 with London-level fares. We will remove a million tonnes of carbon from the Greater Manchester economy. We will retrofit over 12,000 domestic properties,” he said.

“If you sign this deal with us, you can then say: right, we backed Andy Burnham and Greater Manchester with the money and the powers to do something that he says is levelling up.”

If “I don’t do what I’m saying and I’m full of bluster – as they would probably think – then they can call that out” but “if it does start to happen, and yellow and black buses with bees on them start appearing, the north of England will have a very visible sign of levelling-up at its heart”.

As Mr Burnham set out his pitch for extra money and powers, Mr Khan said London must not be ignored.

At a separate fringe event, the London Mayor said: “Some people in Lewisham are as deprived as some people in Liverpool, some people in Stratford are as deprived as people in Sheffield, some people in New Cross are as deprived as people in Newcastle.

“I don’t think the way to make our country more equal is by making London poorer.

“I think one of the things we have got to do is remind our friends from the north, in our own party, why London-bashing, talking London down, is not a sensible way to have a national recovery.

“The message to those in our party who think it plays well slagging off London is you will not get a national recovery without a London recovery.”