Many more deaths would follow before a vaccination programme began to take effect, England's chief medical officer said.
Britain has the world's fifth highest toll from Covid-19 and reported a further 1631 deaths and 20,089 cases on Tuesday.
The 100,162 deaths are more than Britain's civilian toll in World War 2 and twice the number killed in the 1940-41 Blitz bombing campaign.
"It's hard to compute the sorrow contained in that grim statistic, the years of life lost, the family gatherings not attended, and for so many relatives the missed chance, even to say goodbye," Prime Minister Boris Johnson said.
"We will make sure we learn the lessons and reflect and prepare," said Johnson, whose government has faced heavy criticism for its handling of the crisis.
"On this day I should just really repeat that I am deeply sorry for every life that has been lost and of course as Prime Minister I talk full responsibility for everything that the government has done.
"What I can tell you is that we truly did everything that we could and continue to do everything that we can to minimise loss of life and minimise suffering in what has been a very, very difficult stage... and crisis for our country. And we will continue to do that - just as every government that is affected by this crisis around the world is continuing to do the same."
England, by far the most populous of the United Kingdom's four nations, re-entered a national lockdown on January 5, which includes the closure of pubs, restaurants, non-essential shops and schools to most pupils. Further travel restrictions have been introduced.
In December, Britain became the first country in the world to approve Pfizer's Covid-19 vaccine. It has set itself the task of offering vaccination to everyone 70 and over, those who are clinically vulnerable, frontline health and social care workers and older adults in care homes by mid-February.
Up to Monday, a total of 6,853,327 people had received a first dose and 472,446 a second dose.
The government has said the vaccination rate and the success of the vaccinations are key to being able to ease restrictions as Britain battles with the highest deaths per 100,000 people in the world, according to data compiled by Johns Hopkins University.
"Unfortunately we're going to see quite a lot more deaths over the next few weeks before the effects of the vaccines begin to be felt," Chris Whitty, England's chief medical officer said.
New variants have also alarmed scientists, and Johnson has warned the prospect of a "vaccine-busting" variant could mean that lockdown measures are needed for longer.
Britain is due to announce whether it will also bring in mandatory quarantine in hotels for some or all arrivals and has warned the public not to book summer vacations.
"The government is looking at, as the prime minister has confirmed, the hotel quarantine policy, and we'll make an announcement on this in the appropriate way," junior minister responsible for vaccine deployment Nadhim Zahawi said.