Labour will try to move the national debate to the NHS by backing an anti-privatisation bill as Ed Miliband comes under renewed pressure over a record low personal rating.

Lord Prescott, the former deputy prime minister, used his column in the Sunday Mirror to complain that it seemed strategy was “driven by the pointy-heads not the lionhearts”.

“In these last six months we need passionate campaigners to sell our popular policies,” he added.

Andy Burnham, the shadow health secretary, will be in Rochester to support Naushabah Khan, the party’s byelection candidate, who will challenge her rivals to say they would use their first day as an MP to support a Labour-backed bill to repeal some of the coalition’s health reforms.

Labour is trying to focus debate on the NHS amid fresh worries over Miliband’s public popularity, with a YouGov survey finding he had less support that Nick Clegg, the Liberal Democrat leader.

The NHS is likely to figure heavily in campaigning over the next six months, as surveys show it is near the top of people’s concerns and they associate Labour with protecting the health service.

Burnham will say that there will be a vote on Labour MP Clive Efford’s bill on 21 November – the day after the byelection – which will be heavily backed by the leadership. This would exempt the NHS from the EU-US trade treaty known as TTIP, repeal the ‘section 75’ rules that force compulsory tendering of all NHS contracts, remove the freedom that allows NHS hospitals to earn up to 49% of their income from treating private patients, and restore the secretary of state’s responsibility for the NHS.

Burnham said: “This is a unique situation because the bill is coming on to the table the day after the byelection. We’ve checked with the parliamentary authorities and we’ve been assured that the winning candidate could be sworn in during the morning and vote on the bill after that. Our candidate Naushabah would do that and will challenge those from the other parties to say they would do the same.”

He said it was hard to imagine that any Labour MP will not turn out to support Efford’s bill and challenged coalition MPs to take their last chance to admit that their health reforms had been a mistake by backing it.