Prime Minister Boris Johnson said he took "full responsibility" for the government's actions, saying: "We truly did everything we could."
"I'm deeply sorry for every life lost," he said.
A total of 100,162 deaths have been recorded in the UK, the first European nation to pass the landmark.
The UK is the fifth country to pass 100,000 deaths, coming after the US, Brazil, India and Mexico.
It follows a surge in cases last month, leaving the UK with one of the highest coronavirus death rates globally.
The number of cases in the UK has been falling in recent days, but the number of people in hospital remains high, as do the UK's daily death figures.
Earlier, figures from the ONS, which are based on death certificates, showed there had been nearly 104,000 deaths since the pandemic began.
The government's daily figures rely on positive tests and are slightly lower.
A further 20,089 coronavirus cases have also been recorded.