The fall in cases comes amid speculation that students will have to prove that they are fully vaccinated in order to attend lectures from the autumn term, something which Downing Street has so far not ruled out.
Another 24,950 infections were reported by the Government on Monday, the sixth consecutive day of falling figures, and down from 51,870 ten days earlier.
It is currently too soon to see if last Monday’s so-called ‘Freedom Day’ has had an impact on infection rates, although Number 10 said the decline is “encouraging”.
“Throughout the pandemic we have always said it’s encouraging when cases are falling,” the Prime Minister’s deputy official spokesman said.
But the pandemic “is not over” and “we should still expect to see a rise in case numbers given the move to Step 4 last week”.
“The Prime Minister thinks we’re not out of the woods yet,” the spokesman told reporters in Westminster.
Universities are monitoring developments after reports emerged that students may need to show proof of two jabs next year, and a Number 10 spokesman said “we are still looking at the scope for vaccination certifications.”
Bradford University said they “strongly advise getting both doses of the vaccine when offered, wearing masks in busy areas, twice-weekly testing and self-isolation where necessary, in addition to giving others space, mixing outdoors rather than indoors wherever possible and observing guidance around hand sanitising.”
Asked if there was concern about take-up of the vaccines in younger age groups, the spokesman said: “I think you continue to see more and more young people coming forward to receive the vaccine, both in terms of first doses and now second doses.
“Of course, we want to see more people come forward to receive it.
“We would like to see everybody who is invited to come forward and receive the vaccination to do so. That’s the message we continue to try and give to young people.”
A survey released on Monday suggested that young people are not wearing masks as often as they were before restrictions changed across England last week, but figures have stayed stable among other age groups.
The data from YouGov found 46% of 18 to 24-year-olds said they wore a face mask in a public place in the last two weeks, compared to 58% on July 16 and 64% on June 2.
The pollster also said young people were less likely to be fully vaccinated and more likely to have disabled their NHS Covid-19 app.