"A legacy of poor decisions" by the UK before and during the pandemic led to one of the worst death rates in the world, scientists have said.
Labour also criticised "monumental mistakes" by the prime minister in delaying acting on scientific advice over lockdowns three times.
After UK deaths passed 100,000, Boris Johnson said he took "full responsibility" for the actions taken.
But he said it was too soon to learn the lessons from the pandemic response.
Prof Linda Bauld, public health expert from the University of Edinburgh, said the UK's current position was "a legacy of poor decisions that were taken when we eased restrictions".
She told the BBC the lack of focus on test and trace and the "absolute inability to recognise" the need to address international travel had also led to a more deadly winter surge.
Prof Sir Michael Marmot, who carried out a review of inequalities in Covid-19 deaths, said the UK had entered the pandemic "in a bad state" with rising health inequality, a slowdown in life expectancy improvements and a lack of investment in the public sector.
Shadow health secretary Jonathan Ashworth rejected Mr Johnson's claim that he had done "everything we could" to minimise the death toll, adding: "I do not accept that."
He said the prime minister had been given scientific advice to impose lockdowns and "pushed that back" - not only in March but again in September and December.
The government also failed to create a working contact-tracing system, did not introduce effective health controls at the borders and still did not offer "proper sick pay", he said.
At Prime Minister's Questions, Mr Johnson said: "I mourn every death in this pandemic and we share the grief of all those who have been bereaved. I and the government take full responsibility for all the actions we have taken to fight this pandemic."
He said there would be time to reflect on the decisions taken, but he did not think the right time was in the middle of the pandemic when "37,000 people are struggling with Covid in our hospitals".
The government needed to focus on keeping the virus under control and continuing the fastest vaccine roll-out in Europe, he said.
He said his message to grieving families was that he "deeply, personally" regretted the loss of life and that the best way to honour the memory of those who had died and honour those who were currently grieving was "to work together to bring this virus down, to keep it under control in the way that we are".
Asked about the government's "legacy of poor decisions", Mr Johnson said ministers followed scientific advice and did everything they could to minimise suffering. He said there were "no easy solutions" but the UK could be proud of its efforts to distribute the vaccine.
After leading a minute's silence in the Scottish Parliament, First Minister Nicola Sturgeon said she was "truly sorry" for any mistakes, as Scotland recorded a total of 5,888 deaths within 28 days of a positive Covid test.
She said the government did everything it could, but added: "I don't think any of us, reflecting on numbers like these, can conclude that we have always succeeded."
Next month, the prime minister hopes to publish a document giving details of the criteria he will use to start lifting the lockdown, a senior government source told the BBC.
It will include factors such as the number of hospitalisations and deaths, the progress of the vaccination programme, any changes to the virus and the impact easing restrictions might have on the epidemic - but will be dependent on emerging data about how effectively the vaccine stops the virus spreading.
The UK is the fifth country to pass 100,000 deaths, coming after the US, Brazil, India and Mexico.
A scientist advising the government has warned the UK could face as many as 50,000 more coronavirus deaths.
Prof Calum Semple, a member of the Scientific Advisory Group for Emergencies, told the BBC's Newsnight: "It would really not surprise me if we're looking at another 40-50,000 deaths before this burns out.
"The deaths on the way up are likely to be mirrored by the number of deaths on the way down in this wave. Each one again is a tragedy and each one represents probably four or five people who survive but are damaged by Covid."
He said the UK had experienced some "bad luck" with the emergence of a new, more transmissible variant but had also suffered from "decades of underinvestment" in the NHS and "a public health authority that's been eroded" .
Meanwhile, Archbishop of Canterbury Justin Welby and Archbishop of York Stephen Cottrell asked people, regardless of whether they had faith, to reflect on the "enormity" of the pandemic and join in a "prayer for the nation" at 18:00 GMT every day from 1 February.
They said the death statistics were were not "just an abstract figure", saying: "Each number is a person: someone we loved and someone who loved us."
Muslim leaders backed the call for a daily prayer. Qari Asim, chair of the Mosques and Imams National Advisory Board, said Muslims and wider black, Asian and minority ethnic communities had been disproportionately affected by the "tsunami of pain, grief and devastation" - with many unable to properly mourn due to Covid restrictions.
On Tuesday, a further 1,631 coronavirus deaths were recorded, taking the total number of people who had died within 28 days of a positive test to 100,162.
Separate figures from the Office for National Statistics, which are based on death certificates, show there have been nearly 104,000 deaths since the pandemic began.
A further 20,089 coronavirus cases were recorded on Tuesday, continuing a downward trend in the number of UK cases seen in recent days. The number of people in hospital remains high, as do the UK's daily death figures.
Speaking alongside the prime minister, England's chief medical officer Prof Chris Whitty said the number of people dying would come down "relatively slowly" over the next two weeks - and would probably "remain flat for a while now".
Elsewhere, bereavement support charities have written to the health secretary calling for more funding in the light of what they call "the terrible toll of 100,000 deaths".
The National Bereavement Alliance, representing a range of charities, said many families had been unable to be with loved ones as they died or to support one another.
They called for £500m allocated to mental health in England to be used to support the bereaved.
Minister for bereavement Nadine Dorries said the government had given more than £10.2m to charities since March to ensure services were available to those who needed them.
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