Ten new mass Covid vaccination centres are to open in England from Monday, as the government bids to meet its target of offering 15 million people in the UK a dose by 15 February.
Blackburn Cathedral and St Helens Rugby Ground are among the venues chosen to join the seven hubs already in use.
NHS England said the new centres would offer "thousands" of jabs a week.
It comes as a further 324,233 vaccine doses were administered across the UK, taking the total above 3.5 million.
As the latest figures were announced on Saturday, Prime Minister Boris Johnson tweeted his thanks to "everyone who is helping in this fantastic national effort".
More people (3.5 million) have now received a Covid vaccination in the UK than have tested positive (3.3 million) for the virus. However, it is believed there have been many more cases than have been recorded, as mass testing was not available during the first peak last spring.
The government has promised all the over-70s, the extremely clinically vulnerable and frontline health and care workers - about 15 million people - will be offered a jab by mid-February.
In a video call with NHS staff involved in the vaccine rollout, the Duke of Cambridge encouraged members of the public to get the jab.
"I know what a massive difference it's going to make for everyone," he said. "My grandparents had the vaccine and I'm really proud of them for doing that."
And the government urged the public to "play their part" in supporting "the largest vaccination programme in British history", including helping people attend their appointments.
Health Secretary Matt Hancock asked people to commit to three pledges to "help out", "join up" and "stay informed" during ongoing efforts to vaccinate, run clinical trials and share accurate health advice.
Where will the new mass vaccination centres be?
- Bournemouth International Centre, Dorset
- Taunton Racecourse, Somerset
- Blackburn Cathedral, Lancashire
- Salt Hill Activity Centre, Berkshire
- Norwich Food Court, Norfolk
- The Lodge in Wickford, Essex
- Princess Royal Sports Arena, Boston, Lincolnshire
- St Helens Rugby Ground, Merseyside
- The park-and-ride at Askham Bar, York
- Olympic Office Centre in Wembley, north London
The seven hubs already in use are in: Etihad Tennis Centre, Manchester; Epsom Downs Racecourse, Surrey; Robertson House, Stevenage; Centre for Life, Newcastle; Ashton Gate Stadium, Bristol; Millennium Point, Birmingham; ExCel, London.
Writing in the Sunday Express, Mr Hancock said: "We can see the way out of this pandemic. We are nearly on the home straight."
He added that vaccines were being rolled out to as many vulnerable people as possible, saying "we expect tens of millions of people to be vaccinated by the spring".
Asked about reports that the government believes all over-18s could be offered the jab by the end of June, Foreign Secretary Dominic Raab told Sky News that September remained the target but "if we can do it faster than that, then great".
He said the plan was still to vaccinate 15 million people by 15 February - 88% of those most at risk of dying from the virus - followed by a another 17 million in the spring, covering 99% of those most at risk.
People aged 80 or over, who live up to a 45-minute drive from a centre, are now being offered the choice of arranging a jab at one of the 17 centres, or at a pharmacy site through the national booking service.
Anyone not wanting to travel can wait to be contacted by their GP-led vaccination service or hospital.
Some 641,000 invitations were sent out last week and another 380,000 were due to land on people's doormats this weekend, NHS England said, with another half a million letters to go out this week.
According to the Department of Health and Social Care, around 45% of those aged 80 and over have been vaccinated.
Prof David Salisbury, a former director of immunisation at the Department of Health, said the campaign had received a boost because vaccinators had discovered they were able to get six or even seven doses out of vials which were labelled as containing five doses.
He told BBC Breakfast that the speed of the vaccination effort depended on how much manufacturers could supply, but this was an "exciting" development that would allow people to be get the jab more quickly.
GP surgeries could avoid waste by calling up their practice lists to ask people living nearby to come in for a last-minute appointment and use leftover doses, he said.
In addition to the mass vaccination hubs, there are around 1,000 GP-led surgeries and more than 250 hospitals providing jabs.
DHSC said people could back "the national effort" by committing to the government's pledges request.
The department said they can "help out" through supporting family and friends attending vaccine appointments or becoming an NHS volunteer responder, and "join up" to Covid-19 treatment clinical trials.
People can also help others "stay informed" by sharing accurate NHS advice and being alert for Covid vaccine scams.
The ongoing vaccine drive comes as a further 1,295 deaths were reported within 28 days of a positive Covid test - the third-highest daily total since the pandemic began.
While daily figures can fluctuate due to delays in reporting, the seven-day average of Covid deaths in the UK has now risen slightly to 1,103.
For cases, however, there has been a drop in the seven-day average, with the figure now at 48,565.
A further 4,262 people have been admitted to hospital with the virus, taking the total to 37,475.
Dr Yvonne Doyle, medical director for Public Health England, said the "continuous rise in cases and deaths should be a bitter warning for us all".
"We must not forget the basics," she added. "The lives of our friends and family depend on it. Keep your distance from others, wash your hands and wear a mask."
In other developments:
- A financial support scheme for airports in England will open this month, the government says, after new Covid travel curbs were announced
- More than half of the Church of England's 14,000 parishes will not open for Sunday services later, as places of worship are hit hard by the pandemic
- Children in England will be able to access books online free during school closures via a virtual library
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