The government is "drawing up other options" before making a decision on whether to completely lift COVID restrictions on 21 June, Sky News understands.
A government figure said that while Number 10 was still planning to go ahead with the final step in the roadmap, it is waiting for more data before taking any decisions.
"It would be remiss of us to take a decision without a full set of data as evidence," said one government figure.
"Of course officials are drawing up other options but we are still expecting to be in a place to go ahead on June 21."
Options under discussion are said to include:
• Retaining the wearing of face masks in certain settings
• Continuing the work from home advice, even as the hospitality sector opens up
• A slight delay to the unlocking, pushing step 4 into July
Insiders stressed there was no decision made on delaying the easing of lockdown and said Prime Minister Boris Johnson would rather tweak restrictions on 21 June than push the date back.
Until now, the government has only ever said there is "nothing in the data" to suggest ending lockdown should be delayed.
Conservative MP Andrew Bridgen told Sky News the "public appetite" for restrictions could "wane very quickly" if all measures are not removed on the 21st.
"None of the variants are resistant to the vaccine," he said. "We can't sit in lockdown measures waiting for something that might or might not happen decades in the future."
Mr Bridgen said he thought the prime minister wanted to return people's "liberties", adding that renewed freedom was "good for the economy, for wellbeing".
"(People will) feel an awful lot better still when we have the final COVID restrictions lifted on 21 June," he said.
"Lockdowns were there to protect the NHS. We know hospitalisations are a fraction of what they were at the peak. We've been told we've got to get used to living with this virus. Living with the virus doesn't mean we have to be in lockdown forever - that's not a solution."
The British Beer & Pub Association has warned that thousands of pubs "could still be lost forever" if there is a delay, even though indoor service returned on 17 May.
Figures suggest that pubs suffered a 20% fall in trade in the first week after reopening compared with the same period before the pandemic - and if this continues, the average venue could lose £94,000 in turnover a year.
This would mean that the typical pub would need to sell close to 25,000 additional pints over a 12-month period to make over the shortfall.
At present, pubs are required to ensure social distancing of at least one metre is in place. Businesses can also only operate with table service, and group sizes indoors are limited to six people.
However, epidemiologist Dr Adam Kucharski said he was "nervous" about the idea of unlocking later this month amid the spread of the Delta (Indian) variant.
"I think we have to accept the equation has changed here - we are not facing the virus that we were facing two months ago," he told BBC Radio 4's Today programme.
"If we were facing the B.117 (Kent) variant as the dominant one, the fact it (the vaccines) is working very well, case numbers are coming down nicely, we could have some more confidence that there could be reopening without seeing those surges.
"But we're not. Everyone is tired of this pandemic, they want this transition back to normality and that will happen, the effectiveness of two doses of the vaccine will eventually get us there.
"But if say in two weeks we're in a situation where hospitalisations have been rising, where local health systems are coming under pressure, I think it will be quite difficult to justify adding more transmission to that kind of situation."
The comments come after data from the Francis Crick Institute suggested reducing the gap between vaccine doses was more effective, with a study finding that after one Pfizer jab, people are less likely to develop antibody levels against the Delta variant as high as those seen against the previously dominant Kent (Alpha) strain.
Dr Rosalind Eggo, of the Scientific Pandemic Influenza Group on Modelling (Spi-M) advisory panel, said "very early evidence" showed the current vaccines "don't work quite as well against the Delta variant", saying it was vital to increase the rate of second jabs.
She told BBC's Newsnight: "Getting those second doses up, pushing that number up as high as possible is really important."
Concerns have been raised after official data for England showed that COVID-19 cases in the community rose by 76.5% in one week.
The Office for National Statistics (ONS) has estimated that 85,600 people in the country had COVID-19 in the week to 29 May, the highest level since mid-April.
Yesterday, the UK recorded 6,238 new confirmed coronavirus cases - the highest level since late March.
Analysis: Talk of roadmap delays are about preparing a hopeful nation for bad news
By Nick Martin, politics and people correspondent
You might be wondering why we're all suddenly talking about a delay to the final stage of lockdown lifting on 21 June.
That date is supposed to be the big one, when masks and social distancing are scrapped.
But it appears the government is drawing up a contingency plan in the event that a change of course is needed.
There are a few things to consider here.
Cases of COVID are rising, but crucially hospital admissions and deaths have, thankfully, remained low. That shows the vaccines could be breaking the link between infection and deaths.
But variants of the virus are threatening the lockdown easing roadmap; if new mutations can evade the jabs then that would be a significant justification to slam on the breaks.
So the government, behind the scenes, has tried to gauge reaction to such an unpopular move.
As the weekend began, journalists were briefed by government insiders about the possibility of a "contingency plan" - a need to make sure there's nothing worrying in the data that might be a cause for concern.
In other words, preparing a hopeful nation for some bad news.
The problem is the Delta (Indian) variant. Boris Johnson has been widely criticised for not shutting the UK's borders to passengers arriving from India early enough - a move that could arguably have slowed the further spread of the variant.
If this was to become the reason for delaying lockdown easing it could prove damaging to the government.
So on the one hand ministers say everything is on track, while suggesting behind the scenes that a change might be on the cards.
The truth is that the data on which the government will base its decision about 21 June will not be available until next week - and a lot can happen between now and then.