Angela Rayner has said the very survival of the Labour party is at stake and warned Keir Starmer that he “cannot go through the motions” in the face of declining support.

In a speech at campaign group Mainstream’s spring reception, the former deputy prime minister said she believed the government was “running out of time” to show it can deliver the change that the public needs.

In what will be seen as a major intervention, Rayner said it was “un-British” to move the goalposts on indefinite leave to remain, putting her at odds with the government’s key immigration proposal of increasing the standard qualifying period for permanent residence from five to 10 years.

Rayner said on Tuesday evening in London: “It is down to us to rebuild this nation and this party – the question is are we up for this fight? I know we in this room are.

“As a party, and as a movement, we cannot hide, we cannot just go through the motions in the face of decline. There’s no safe ground and we’re running out of time.

“The change that people wanted so desperately needs to be seen, it needs to be felt. And we have to show that it is a Labour government that will deliver it.”

Currently, people can apply for indefinite leave to remain after five years, giving the right to live, study and work in the UK permanently.

On the planned changes to the immigration system, Rayner said: “We cannot talk about earning a settlement if we keep moving the goalposts. Because moving the goalposts undermines our sense of fair play. It’s un-British.

“Let us be a country that has sustainable economic migration rules, but one that upholds the British values we want all who live here to respect.

“Not special treatment. But the stability and a fair pathway forward after the sacrifices many have made to build a lawful life in the UK.”

Rayner also condemned the policies of Reform and the other opposition parties, which she accused of pitting “people against one another for political gain, and who stoke fear through blame”.

The MP for Ashton-under-Lyne, who resigned as deputy prime minister and housing secretary last September, said: “Our very flags twisted into symbols of division, not the unity our values embody. This rhetoric isn’t just false – it’s deeply dangerous.

“And we know why they want it to be the national conversation. Because when it comes to our economy, they have no answers. Promises but no plans. Not for change. Not for fairness.

“They will agree the system is rigged, but they are on the side of those who rigged it.”

Last month, Maryam Eslamdoust, the general secretary of the Transport Salaried Staffs’ Association, called for Rayner to replace Starmer as Labour leader.

Last month the Guardian revealed an unfinished website claiming to launch Rayner’s Labour leadership campaign had been published temporarily in January, prompting further speculation that the former deputy prime minister could be gearing up for a contest to replace Starmer.