Moving to the right on immigration to counter Ukip would be a disaster, the Labour MP Diane Abbott has said. The London mayoral candidate accused certain MPs within her party of hysteria and trying to “out-Ukip Ukip”.

She said: “There is a feeling that everyone has got to toughen up on immigration, have a much harsher rhetoric. Part of this is the notion you can do something about EU freedom of movement. The truth is, you can’t. Freedom of movement is an absolutely central component of the EU.

“I think [David] Cameron and people close to Cameron saying we are going to introduce quotas is just spin. In reality, they won’t be able to do it. You can’t out-Ukip Ukip. Certainly if the Tories want to do it, then that is up to them. Of course there is a problem with low wages and insecurity. But you deal with that, you don’t scapegoat migrants.”

Asked on Murnaghan on Sky News whether she would make that argument to the Labour leader, Ed Miliband, she replied: “I have said it to Ed. The trouble is that some Labour MPs are getting hysterical. They are repeating things that aren’t true. I have said to Ed Miliband moving to the right on immigration to counter Ukip will be a disaster.”

The Hackney North and Stoke Newington MP was recorded making a similar point at a rally staged by the Labour Assembly Against Austerity last week.

She said: “You have Labour members of parliament talking nonsense and recycling urban myths about immigration. So I think rather than do what a lot of people at the top of the party – well, some of the people at the top of the party – want to do, which is to chase after Ukip in this downward spiral on anti-immigrant rhetoric, but to deal with the real issues that our people mention on the doorstep, we have to contest Ukip. We have to offer people hope by contesting the Tory austerity agenda.”

Her fellow Labour MPs Ian Lavery and Chris Williamson also spoke at the meeting, a day after Miliband appealed for unity. Williamson called for a return to policies of the 1970s, claiming it was “absolutely abundantly clear” that neo-liberal economics did not work.

According to the Sunday Times, he was recorded saying: “We saw what it did in Latin America when it was inflicted at the point of a gun and we have seen a democratic Bolivarian revolution has absolutely transformed the lives of people in Latin America. Wouldn’t we do well to actually learn some lessons in terms of policy inspiration for the Labour party to look at the democratic Bolivarian revolution?”

He was referring to the nationalisation movement pioneered by Hugo Chávez, the late socialist president of Venezuela, and named after the 19th-century revolutionary Simon Bolivar.

One policy Miliband should consider, Williamson said, was banning shareholders from receiving a dividend unless their companies pay the living wage.

Lavery was heard saying: “We need to represent the people who established the party, the same principles applied in the early 1900s when the Labour party was brought into being … to support working people. People who were vulnerable, people who didn’t have a voice. And the principles of the party should be exactly the same now.”

Meanwhile, the shadow health secretary, Andy Burnham, who stood against Miliband for the party leadership and was seen as a potential successor to him, has ruled out another bid for the top job.

He said: “I am a Labour loyalist to my core. I am loyal to the leader, and the leader of our party Ed Miliband has said the NHS will be his big priority going towards this election.”

Asked whether he would rule out standing for the leadership in due course, he told BBC1’s Andrew Marr Show: “I rule it out.”