Ministers want all over 50s to have received a second coronavirus jab before a further easing of lockdown restrictions on 21 June.
The new target comes amid growing fears over the highly transmissible strain of the disease first identified in India.
The government is coming under increasing pressure from experts to consider a delay to its 21 June deadline.
Linda Bauld, professor of public health at the University of Edinburgh, today described the date as “too early” and warned it could lead to deaths that were otherwise preventable.
Ministers announced on May 14 that the gap between vaccines would be slashed from 12 weeks to just eight for the over 50s and the clinically vulnerable, as fears over the impact of the Indian strain grew.
Vaccines minister Nadhim Zahawi has now said that the government “hope to get two doses… (delivered to) all over 50s before the 21st of June”.
All legal limits on social contact are due to be lifted in England on 21 June, a step Boris Johnson has described as “irreversible” once taken .
But ministers are now engaged in a race with the new strain, with almost half of all new cases thought to be the Indian variant.
One bright spot on the horizon is that data suggests that two vaccinations are effective against the new strain.
Public Health England statistics show the majority of those who have been infected have not been vaccinated.
Last week the prime minister himself appeared to admit his 21 June plans now hang in the balance. While he said he “didn’t see anything currently in the data” to derail the June reopening, he added “but we may need to wait.”
Prof Bauld told Sky News: “I really think that it is too early to be charging ahead. I would like to see several more weeks’ data.”
The planned date is “very ambitious”, she said, adding: “The 21st of June is very soon and I think to avoid more preventable deaths… we really need to be cautious at the current time.”
Dr Mike Tildesley, from the University of Warwick and a member of the Scientific Pandemic Influenza Group on Modelling (Spi-M) Government advisory panel, said “an awful lot of uncertainty” surrounded the plans.
He told LBC: “I think there’s still an awful lot of uncertainty… that needs to be resolved over the next couple of weeks before the government make that decision.”
Chris Hopson, chief executive of NHS Providers which represents NHS trusts, said a “much better quality of debate” was needed on the implications of easing restrictions.
He warned the situation had changed dramatically since earlier points in the pandemic with hospitals currently “going full pelt” to tackle waiting lists built up during the crisis
They did not have the space for a significant increase in Covid patients, he said.
Writing in The Observer, Labour leader Sir Keir Starmer said “weak, slow decisions” by the government on border policy had allowed the Indian variant to spread.
He added that the “single biggest threat” to England’s full reopening was “the government’s incompetence”.