Former Health Secretary Matt Hancock mocked people in quarantine during lockdown and suggested getting "heavy with the police", leaked texts show.
Messages published by the Telegraph seem to show Mr Hancock joking with a top aide about travellers being "locked up" in "shoe box" hotel rooms.
He also suggests police chiefs should be told to enforce rules more strongly.
Other texts show Boris Johnson describing a £10,000 fine on two people who broke quarantine rules as "superb".
They are the latest in a slew of revelations to come from the leak.
The messages, which the BBC has not independently verified or seen in their full context, were among some 100,000 sent between ministers and officials during the pandemic, and handed to The Telegraph by journalist Isabel Oakeshott.
Ms Oakeshott, a longstanding critic of lockdowns, was given them while helping Mr Hancock write his book, Pandemic Diaries.
He has described the leak as a "massive betrayal" used to produce "a partial, biased account to suit an anti-lockdown agenda".
But the messages do give an insight into the inner workings of the government as it grappled with containing the spread of Covid-19.
In an exchange on 16 February 2021, Simon Case, who holds the most senior position in the civil service as cabinet secretary, asked Mr Hancock if he knew "how many people we locked up in hotels yesterday".
The message was sent the day after England introduced mandatory quarantine for arrivals from 33 high-risk countries.
Mr Hancock replied: "None. But 149 chose to enter the country and are now in quarantine hotels due to their own free will!"
"Hilarious," Mr Case responded.
Mr Hancock also wrote: "We are giving big families all the suites and putting pop stars in the box rooms."
People affected by the policy at the time described the way it was implemented as a "mess" and being kept in a hotel as like living in a "prison"
In an earlier exchange, on 28 August 2020, Mr Case, then the Downing Street permanent secretary, asked Mr Hancock "who actually is delivering enforcement", apparently during a discussion about lockdowns.
Mr Hancock replied: "I think we are going to have to get heavy with the police."
In another message in January 2021, Mr Hancock appears to be describing what was talked about at a meeting of senior figures, including the prime minister.
After summarising a discussion about the enforcement of lockdown, he says: "The plod got their marching orders."
During the pandemic, the police were often criticised for enforcing lockdown rules in a way that many considered over-zealous, with fines issued to dog walkers and protesters.
But surveys at the time suggested most people supported how the police were enforcing the new rules.
Labour's shadow home secretary Yvette Cooper said the exchanges revealed the "arrogance and shameful lack of respect" of ministers towards the police.
"At the same time as they were flagrantly breaking the law themselves with their lockdown parties, they were demanding stronger enforcement by the police on everyone else."
In March 2021, Mr Hancock also texted then-Prime Minister Boris Johnson a link to a news article about two people who were fined £10,000 each for failing to quarantine after returning from Dubai.
Mr Johnson replied: "Superb".
Other leaked messages reported by The Telegraph appear to show:
- Mr Hancock's team asked if they could "lock up" former Brexit Party leader Nigel Farage after he tweeted a video of himself at a pub in Kent
- Social care minister Helen Whately joked about celebrating Piers Morgan's departure from Good Morning Britain
The Liberal Democrat deputy leader, Daisy Cooper, said: "This lifts the lid on the contempt that Boris Johnson and his Conservative cronies had for the British public during the pandemic.
"They mocked and joked while breaking the rules we were all required to follow.
"The Covid inquiry must be able to get to the bottom of this sorry saga in our country's history as soon as possible. The public deserves the truth and bereaved families deserve justice."