Andy Burnham has said he will not try to return the UK to the EU, saying Britain would be stuck in “a permanent rut if we’re just constantly arguing”.

In his first major speech since announcing his byelection run, the mayor of Greater Manchester said he would have a “relentless domestic focus” in Makerfield, saying: “Let’s fix our own country. Let’s get it working again. Let’s get it back to where people want it to be.”

The comments came after his potential leadership rival Wes Streeting said the UK should rejoin the EU, his first big intervention since resigning as health secretary. Burnham said: “My view is that Brexit has been damaging, but I also believe the last thing we should do right now is rerun those arguments.”

Burnham said he wanted to turn the national spotlight on Makerfield and the north-west during his byelection campaign – saying his fight against Reform UK would centre on what could change for places like that.

“I want to say sorry to the residents of the Makerfield constituency, for the circus that is about to arrive in town and some of the inconvenience they will experience as a result,” he said.

“But on the other hand, I want to say this to them as well: I hope you feel it’s a good thing as well, that the places that make up this constituency, long forgotten by national politics, finally are at the centre of the national debate. And for the places of this constituency again, you could read many of the similar places in yours.

“Let’s get them at the top of the agenda for the first time in a very long time. And that’s what this byelection will hopefully succeed in doing. My plan for Makerfield will be ambitious and it will show how we lift up its people and places over the next decade.”

Burnham said he would make the argument that places such as Makerfield had been failed for four decades.

“The deindustrialisation of the 1980s was devastating for places across Makerfield. That was followed by deregulation, privatisation and austerity, he said. “It all adds up to 40 years of neoliberalism that have not been kind to the north of England.

“Forty years of trickle-down economics that did not, in the end, trickle down very much at all to places like Platt Bridge or Hindley. In fact, that system has siphoned wealth out of those places and into the hands of people for whom life was already very good.

“I believe the byelection is very necessary. In my view, the time has come for a much bigger debate about how politics needs to change if it is to work properly for the north of England, because it doesn’t. It doesn’t and this is what we’ve got to focus on. People are losing faith in politics.”