Thousands more people will receive a Covid-19 vaccine this week as seven mass centres open across England.
NHS England said hundreds more GP-led and hospital services would also open later this week.
The government is aiming to vaccinate 15 million people in the UK – the over-70s, healthcare workers and those required to shield – by mid-February.
Health Secretary Matt Hancock will set out the government’s vaccine delivery plan at a press conference later.
He said the proposals would be the “keystone of our exit out of the pandemic”.
The government will also publish its first daily figures which will reveal how many people have been given the vaccine.
Mr Hancock said on Sunday about two million people in the UK had been vaccinated, with some 200,000 jabs administered in England daily.
The vaccine plan will be unveiled after the UK recorded more than 80,000 coronavirus deaths since the start of the pandemic.
In Surrey, which has one of the highest infection rates in the country, a temporary mortuary has been opened as hospital mortuaries have reached capacity.
Almost 200 bodies are being stored at the emergency site, which is a former military hospital, and other local authorities have told the BBC they expect to open similar facilities soon.
On Saturday scientists warned stricter lockdown measures might be needed in England and the health secretary has urged people to follow the spirit as well as the letter of the rules.
Mr Hancock told the BBC’s Andrew Marr Show on Sunday “every time you try to flex the rules that could be fatal” and said staying at home was the “most important thing we can do collectively as a society”.
Under the national lockdown, people in England must stay at home and can go out only for limited reasons such as food shopping, exercise, or work if they cannot do so from home. Similar measures are in place across much of Scotland, Wales and Northern Ireland.
Ministers held two meetings on Sunday to discuss how to enforce the current lockdown measures more strictly and whether even tighter restrictions may be needed.
The vaccination programme is described as the biggest in NHS history, with an aim of offering jabs to most care home residents by the end of January and the most vulnerable by mid-February.
Some 600,000 invites were due to be sent out over the weekend and this coming week to people aged 80 or older who live up to a 45-minute drive from one of the new regional centres.
The new centres will each be capable of delivering thousands of vaccinations each week and will be followed by “dozens more” large-scale sites, NHS England said.
There will be about 1,200 vaccination sites when more GP-led and hospital services open later this week, along with the first pharmacy-led pilot sites, it added.
Vaccines minister Nadhim Zahawi said the government’s vaccine delivery plan would “set out our ambitions for the coming weeks and months as we continue to expand our programme at breakneck speed”.
“It’s been phenomenal to see our extensive preparations come to fruition and from Monday the public will also be able to see exactly how we will ensure they and their loved ones get the vaccine as quickly as possible,” he added.
Prof Stephen Powis, NHS England national medical director, said “increasing supplies” meant the NHS could “open even more vaccination services and protect even more people this week”.
He also called on the public to help the NHS, saying: “Please don’t contact the NHS to seek a vaccine, we will contact you. When we do contact you, please attend your booked appointments.”