Latest government data suggests that more than 39.4 million people had received their first dose by Tuesday –equating to 74.9 per cent of adults.
Matt Hancock, the health secretary, will use a speech on Wednesday to praise the central role of the NHS in the vaccine rollout and say the government "backed lots of horses", investing "at risk" in different projects.
He will be speaking as experts are divided over whether the final stage of the government's roadmap out of lockdown in England can go forward as planned on 21 June due to concerns over the spread of the Indian variant.
Downing Street said the government still sees nothing in the data to suggest the lifting of restrictions will need to be delayed.
Tuesday’s death tally is likely to feed into ministers’ considerations on easing restrictions.
They will also consider that the announcement of zero deaths came after a bank holiday weekend, so there may be a delay in the reporting of the figures.
Later in the week, Mr Hancock will speak at the Jenner Institute in Oxford ahead of the G7 Health Ministers' meeting which will be hosted in the city.
He is expected to say: "Even before the first Covid-19 case arrived in the UK we'd started the work on how to develop, procure and roll out the vaccines that would ultimately make us safe.
"I was told a vaccine had never been developed against any human coronavirus. We dared to believe ... and we started early.
"We put out a call for research in February. By March, we were supporting six different projects, including the Oxford vaccine, alongside the vital work on treatments - including the Recovery trial, which led to the discovery of dexamethasone, the first proven treatment to reduce coronavirus mortality. These two projects, together, have already saved over a million lives."
Mr Hancock will say: "The biggest risk would have been the failure to find a vaccine at all. So we explicitly embraced risk early on. So we backed lots of horses and invested at risk.
"And instead of sitting back and waiting to see which vaccines came off, we were tenacious in helping them to get over the line, drawing on the abundant industry experience in our team."
The health secretary is also expected to outline how the NHS has "deserved every plaudit that has come its way", and talk about the UK's “scientific strength”.
Additional reporting by agencies
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