The Times reports that there are fears that the spread of the new Indian coronavirus variant could "end in tiers", forcing ministers to re-impose local lockdowns.
While Boris Johnson considers this a "last resort", it says, officials have drawn up plans modelled on the Tier Four restrictions introduced in England last year.
The paper reports Mr Johnson has rowed back from the "maximalist" approach he had been considering, which would have dropped the need for face masks in most public places, along with the one-metre plus social distancing rule.
Tory MPs, it reports, are urging the prime minister not to slow down his unlocking plan just for the sake of what it calls a "small band of anti-vaxxers".
The Mail quotes an unnamed cabinet minister who says that 21 June has become the "freedom date...burned on people's brains". But "at last, they get the point", reads the main headline in the Metro, which says even vaccine sceptics are now taking up the jab, including 10,000 people last week in Bolton.
The Daily Telegraph says EU ambassadors will agree tomorrow to allow fully vaccinated British holidaymakers to fly to Europe, without the need for Covid tests or quarantine.
The paper says the bosses of British Airways and Heathrow Airport have urged the government to reveal in advance which countries it's planning to add to its so-called green list - so families can plan ahead for later in the summer.
Heathrow's chief executive tells the Telegraph that the current list of just 12 quarantine-free destinations - most notably Portugal - is leaving passengers with high prices and limited choices, for last-minute bookings.
The Financial Times reports the cabinet is split by a "ferocious" fight over whether to sign off a trade deal with Australia. It says the debate is over whether to grant zero-tariff access to Australian farmers - and risk a backlash from the UK farming industry.
Allowing tariff-free imports of Australian lamb and beef, it reports, would "land hardest" in rural areas such as Scottish and Welsh hill farms.
It's a "100-million-dollar question", one government official has told the paper - with the Environment Secretary George Eustice, and his predecessor, Michael Gove on one side of the issue, and the International Trade Secretary, Liz Truss, and the Brexit negotiator, Lord Frost, on the other.
The Guardian has a front-page story that the Home Office is writing to British citizens with dual EU citizenship, warning them - in error - that they need to apply for settled status.
It says people who've been here for decades have "expressed alarm" at being told they could lose the right to work, benefits, and free healthcare - unless they apply for UK immigration status in the next six weeks.
The Home Office tells the paper that in trying to contact "as many people as possible" about settled status, there may be "a small number of cases" where letters have been sent to someone who's already naturalised as a British citizen. In such cases, it says, no action is required.