The UK should be braced for at least a third wave of the coronavirus pandemic and further lockdowns, a minister has said as Tory sceptics warned they would not vote to extend England’s four-week shutdown. Penny Mordaunt, the paymaster general, told MPs on Tuesday that there could yet be a rolling series of lockdowns – but argued this was not evidence that the measure was ineffective. It came as the former chief whip, Mark Harper, criticised a lack of engagement with Conservative backbenchers before a Commons vote on England’s lockdown on Wednesday, and said the government would be forced to rely on Labour votes to pass any extension beyond 2 December. Ministers expect a moderate number of Conservative MPs to rebel but Labour support means the measures are guaranteed to pass. Speaking in parliament, Mordaunt said the government was “hopeful of being able to unlock in December but they are being driven by the data”. She said cases would inevitably rise after restrictions are lifted, and a high proportion of the population will remain vulnerable to the virus. “That is why some scientists expect a third or more waves of the virus to be managed [with] repeat lockdowns. Others argue that the need for future lockdowns is evidence they don’t work but that’s to misunderstand what they are there to do,” she said. “This approach buys us time and is the optimum use of the healthcare we have in the meantime while capacity is built and vaccines are sought.” Her remarks contrasted with those of Boris Johnson, who was bullish that England’s lockdown would end on 2 December, telling a cabinet meeting on Tuesday that this was a hard deadline to develop a new solution to contain the spread of the virus. The prime minister also appeared to affirm that the government expected the four-week lockdown to be enough to get the virus’s R number below 1 – raising questions as to whether the lockdown would be extended should that not occur. “Once again we are, alas, asking everybody to stay at home to protect the NHS, to save lives, and get the R down below 1. I know we can, I know we will. It’s only just above 1 at the moment,” he said. Harper said he had not received the reassurances he had repeatedly requested about the projections used by Johnson to justify the lockdown. He said he had not yet decided whether to support the government on Wednesday but predicted most colleagues would reluctantly back the plan, though the prime minister would struggle to secure support for any extension next month. “If the government do need to extend these measures, I think it’s very clear that they would end up depending on the votes of the Labour party – and prime ministers who end up depending on the opposition tend to end badly, in my experience.” James Grundy, the MP for Leigh in Greater Manchester – Andy Burnham’s old seat and a Labour stronghold for 114 years until December – said he planned to vote against the government unless financial support improved significantly or there was a clear timetable for a vaccine. “A rolling series of lockdowns might … hold Covid-19 at bay for a few weeks, or months, as the last one did. Then again, it might not. It certainly will cause absolute devastation to every other part of our society though,” he said. Conservative lockdown sceptics criticised the government’s strategy during a debate in Westminster Hall, to which Mordaunt was responding. The backbencher Richard Drax said the government had overreacted to the pandemic. “A draconian, onerous and invasive set of rules and regulations now govern our very existence,” he said. “I cannot recall a moment in our proud island history where our nation has been so cowed to the extent it is now.” The Tory MP Bob Seeley said anyone who believed restrictions would end on 2 December was “living in a parallel universe … You really wonder if the government is losing the plot over this.” Chris Green, the Conservative MP for Bolton, said the response had been “erratic”, and the regional tiered system had not been given enough time to have an effect.