The government's plan is for all Covid-19 restrictions to be dropped on June 21.
The scientists warn of a potential "wave" in cases of the variant first found in India.
A decision about the easing of restrictions in Glasgow is expected by Wednesday with most of mainland Scotland set to move to Level 1 of the tier system on June 7.
Concern over the Indian variant continues as the number of Covid-19 cases rises across the country.
But Paul Hunter, professor in medicine at the University of East Anglia, says the number of Indian variant cases in the United Kingdom has been "doubling every seven to 10 days since the beginning of April and if that isn't exponential growth I don't know what is".
He said the government should postpone unlocking the country by "a few weeks".
"All waves start with low numbers of cases that grumble in the background and then become explosive".
He added: "Although we're seeing rises, we're not quite at that stage where you would call it a third wave".
"One of the most important things for me would be whether we are seeing cases of vaccine failure with the Indian variant, because that would mean that the vaccine programme we are rolling out is less effective than we think it is".
When asked about the possibility of a delay to freedom from restrictions, Environment Secretary George Eustice said nothing could be ruled out.
Eustice said the government had to take things "one step at a time".
But some scientists remain anxious about a recent rise in cases and warn the UK's vaccination programme is offering a "false sense of security" amid a mounting third wave of infections.
"We have to make that judgement a couple of weeks before".
"It will only be by then that we will see the full impact of the latest easements we made on May 17, so I know everyone wants to know what is going to happen but we can't actually make that judgment until we see the impact".
In a bid to stay on track for the roadmap and protect against the Indian variant, ministers now want everyone over 50 to receive their second dose before the final restrictions are lifted next month.