People aged 25 and over in England will be invited to book Covid-19 vaccinations from Tuesday, the health secretary has announced – as questions remain over whether the government’s plan to lift lockdown by 21 June will go ahead.

Speaking in the Commons on Monday, Matt Hancock told MPs: “From tomorrow morning we will open up vaccination to people aged 25 to 29. Over the remainder of this week, the NHS will send texts to people in these age groups and of course GPs will be inviting people in these age groups to come forward.”

Mr Hancock also confirmed that the UK’s medicines regulator has determined that the Pfizer vaccine is “safe and effective” for teenagers 12 years and older.

He added that he would ask the JCVI to come forward with clinical advice on a timetable for vaccinating this age group, which the minister said the government would listen to.

The health secretary added that inoculating school-aged children was increasingly crucial as a large proportion of new cases were being detected in this age group.

The announcements come amid uncertainty over whether the government will be able to proceed with the next phase of its unlocking plan, which is due to take effect in a fortnight. The decisions on whether to lift the last remaining legal restrictions will be announced next week amid growing calls for caution over the emergence of the new Delta variant, which was first identified in India.

Professor Sir David King, former chief scientific adviser to the government and chair of the Independent Sage group, said on Monday the latest data was “evidence of another wave appearing”.

Mr Hancock stressed on Sunday the government was “absolutely open” to delaying the final unlocking if necessary, but said it was too early to make a decision.

A new analysis by the Press Association suggests that around three-quarters of local authorities reported a week-on-week rise in the week to 2 June – the highest proportion since early January. A total of 283 out of 380 areas recorded an uptick in cases, with the greatest numbers in London, northwest England and Scotland.

The government meanwhile estimates that vaccines have prevented an estimated 39,000 hospitalisations and over 13,000 deaths.

Speaking in the Commons, the health secretary said that for now the government wanted schools to resume twice-a-week home testing of children to allow infected pupils to self-isolate with the minimum disruption to education.

And he added that the government was still on track to offer all adults a vaccine by the end of this July.

Mr Hancock said: “Speaking to those directly in their late 20s who will be able to book a jab from tomorrow, and others who might feel that in their age group they are unlikely to die of Covid: the honest truth is the best way for us to get our freedoms back, get back to normal, is for everybody to come forward and get the jab. It really matters that we all come forward and do this because that is the safest way out.”

The new dates in the announcement apply to England, where the NHS is under control of the government in Westminster. Wales is ahead of schedule, and set to offer vaccines for all over 18 from next week.

Labour’s shadow health secretary asked the government to “do more to drive up vaccination rates in those areas that have seen the Delta variant take off and where uptake remains low such as Blackburn, and my own city of Leicester”.

He also suggested “narrowing the timeframe between the first and second dose” due to reduced protection after a first dose against the new variant.

But speaking earlier, Sir David told Sky News: “[There are] 5,300 new cases of the disease per day in the United Kingdom and we’re up about 2,000 on last week.”

“Now we’ve been discussing whether or not we’re going into a serious third wave and I don’t think we can possibly wait any longer – this is the evidence of another wave appearing.

“We know that anyone vaccinated twice is relatively safe against the virus, but let’s not forget the one in 25 new cases are people who have been vaccinated twice – that means 400 new cases a day are people who had the vaccine twice.”

He added: “The number of people in our hospitals, which the government says is relatively stable, it’s 932 per day going into hospital, which is up 65 from last week. It’s not actually stable, it is slowly rising.

“I’m very reluctant to say that we should not go out of lockdown on 21 June, but I think the figures are in now, and it will be wise for the government to announce right away a delay in opening, just so that we can all plan for the post-21 June period.

“I would give a few weeks’ delay and see how the figures are emerging.”

Mr Hancock revealed on Sunday that the Delta variant was about 40 per cent more transmissable than the strain previously prevalent in the UK.

But he said vaccines were “working” and that “very few” people who had been fully vaccinated were ending up in hospital, adding that some under-30s would be invited for their jabs this week.

NHS leaders have said those being admitted to hospital are generally younger and less likely to fall seriously ill.

Ravi Gupta, professor of clinical microbiology at the University of Cambridge, said “a few more weeks rather than months” could be needed before leaving lockdown completely.

He told BBC Breakfast that options could include a modification of a full exit from lockdown. He suggested that this could involve both remote working and continued mask-wearing in workplaces.

Daily reported cases of Covid-19 remained above the 5,000 mark over the weekend, with a further 5,341 lab-confirmed cases recorded on Sunday. Meanwhile, a further four people have died within 28 days of testing positive for Covid-19, as of 9am Sunday.

Additional reporting by PA