Scientists have warned ministers that a third wave of coronavirus may have already begun in Britain, casting doubt on plans in England to lift all lockdown restrictions in three weeks’ time.

Experts cautioned that any rise in coronavirus hospital admissions could leave the NHS struggling to cope as it battles to clear the huge backlog in non-Covid cases.

Downing Street insisted it was too soon for speculation about whether the plan to lift all lockdown rules in England on 21 June could go ahead, prompting calls from the hospitality industry for the government to ensure it provided “advance notice” for struggling businesses of any “lingering” measures.

The vaccines minister, Nadhim Zahawi, refused to deny that some restrictions such as mask wearing and working from home might remain in place to reduce the spread of the virus. Senior scientific advisers believe that, where possible, working from home makes sense beyond June because it would cut the number of people who come into contact with each other.

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Ministers are grappling with whether a rise in cases and further spread of the Covid variant first discovered in India could throw Boris Johnson’s roadmap off track. Despite the progress of the vaccination programme, advisers are unsure to what extent the new infections – which are at levels last seen at the end of March – will translate into hospitalisations and deaths.

Outbreak modellers advising Sage expected a resurgence of infections even before the new variant, called B.1.617.2, was found in the UK. That is because, as restrictions ease, the virus can spread more easily among millions of people who have not been protected by vaccines. Research by Public Health England that suggests the new variant is highly transmissible and partially resistant to vaccines has heightened concerns that a third wave could overwhelm the NHS.

Speaking on the BBC’s Andrew Marr show, Zahawi refused to rule out that the planned unlocking could be tweaked, adding that an announcement will be made on 14 June. “We have to look at the data and we will share that with the country,” he said. “It would be completely wrong for me to now speculate. There are many people watching your programme, in jobs and businesses, who want to basically follow the exact direction the government is giving them whilst taking personal responsibility.

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“At the moment, we don’t have enough data. There are some parts of the country where there’s literally no B.1.617.2 and everything is pretty stable; in other parts of the country it is beginning to overtake the B.1.1.7 variant – the Kent variant.”

The chancellor, Rishi Sunak, was similarly cautious, telling the Mail on Sunday: “We will know more as we approach the date.” The India variant is thought to be driving a rise in cases in parts of the UK and there are signs of a slight rise in hospitalisations. Up to three-quarters of new Covid cases in the UKare thought to be caused by the variant.

Martin McKee, a professor of European public health at the London School of Hygiene and Tropical Medicine, said he believed the third wave had begun.

“We can already see that the current measures are not stopping cases rising rapidly in many parts of the country. This looks very much as if we are now early in a third wave,” he said. “Unless there is a miracle, opening up further in June is a huge risk. The rise in cases we are seeing now should cause a reassessment of the most recent relaxation.”

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Paul Hunter, a professor in medicine at the University of East Anglia, said he was concerned the UK was seeing the early signs of a third wave earlier this month, as it became clear the India variant was spreading in the community.

Prof Ravi Gupta of the University of Cambridge, a co-opted member of the New and Emerging Respiratory Virus Threats Advisory Group (Nervtag), also raised concerns. “If things go as I think they are going to go, we will likely end up with a third wave. It will be a big wave of infections and there will be deaths and severe illness,” he said.

“It will put pressure on the NHS at a time when we are trying to get back to normal and it is going to require a redoubling of efforts from the government to step up vaccination and to look at boosting of waning [immune] responses.”

Gupta said he was in favour of delaying the planned 21 June relaxation in England until the summer holidays, when the chance of spread within educational settings is reduced.

A substantial rise in coronavirus patients would hit the NHS just as staff are facing lengthy waiting lists for delayed procedures. Chris Hopson, the chief executive of NHS Providers, said staff were “going full pelt” to deal with the backlog and did not have the space for a significant increase in coronavirus admissions.

“While it’s great news that the vaccinations are working – and I think that sends us one message in terms of opening up on 21 June – what we mustn’t forget is there are still lots of people who need to be vaccinated, and we know this variant that originated in India is much more transmissible,” Hopson told BBC Breakfast.

Dr William Hanage, a professor of the evolution and epidemiology of infectious disease at Harvard, said the UK’s current approach was not enough to prevent a third wave of infections. “The only question is how consequential it will be in terms of hospitalisations and deaths, and when exactly it happens,” he said. “A full reopening in June is not compatible with controlling the virus.”

Aubrey Allegretti, Nicola Davis and Ian Sample