Chris Whitty has sent a clear message to cut back on socialising in the run-up to Christmas Day, warning that a rise in Covid hospitalisations is “nailed on” after cases hit a record high.

Appearing on Wednesday alongside the prime minister, who has continued to insist formal restrictions on gatherings are unnecessary, Whitty said: “Don’t mix with people you don’t have to.”

He advised the public to “prioritise social interactions that really matter to them”, suggesting work parties may be ill-advised.

Nikki Kanani, medical director for NHS England, said if people were heading to a stadium this weekend, it would be better to go for a booster jab rather than to watch a match.

The government has expanded mandatory mask-wearing and advised the public to work from home where possible – but continued to insist other events such as Christmas parties and school nativity plays should go ahead. The medical advisers’ words will lead to fears of cancellations in the hospitality industry, however.

Whitty was speaking after new UK Covid cases hit a record daily high of 78,610. Pointing to the sharp increase, he said: “I’m afraid we have to be realistic that records will be broken a lot over the next few weeks.”

He added that the UK was being hit by “two epidemics on top of each other” – with Delta variant cases remaining high but stable, while Omicron cases were “rapidly growing”.

NHS leaders warned on Wednesday that the health service was already being hit by increasing numbers of staff falling ill with coronavirus.

Boris Johnson appeared to strike a more upbeat note, highlighting the enthusiasm with which the public have been coming forward for their booster jabs, and claiming “a great national fightback has begun”.Booster vaccines are being rolled out at a faster pace, with 656,000 people receiving their third jab on Wednesday, up by 143,000 from the previous day, and Johnson said people should get fully inoculated as soon as possible, to give Omicron “both barrels”.

He said the NHS was “in a race against time to get those jabs in arms”. From Monday, children aged 12 to 15 will be able to book their second vaccine, and Johnson urged them to do so before schools return after the Christmas break.

The prime minister reiterated his insistence that this Christmas will be better than last year’s, when last-minute limits were imposed on household mixing – though he added that his own plans were modest, and he expected to be working throughout.

Whitty’s cautious message was echoed by Kanani, who said she would be “really careful” in the run-up to Christmas Day, “so I can get those special moments with my family”. She added: ”I know that’s what everyone will choose to do if they can.”

Whitty’s warning to avoid unnecessary socialising is likely to intensify the pressure on the Treasury to fund a new package of support measures for hard-hit sectors including hospitality, with restaurants and hotels already saying bookings had plunged.

The British Chambers of Commerce president, Ruby McGregor-Smith, said the comments would have an “enormous impact,” adding: “Businesses now face the two-punch combination of serious issues with staff absence and plummeting consumer confidence.”

One government source said there was “a lot of working going on” in relation to how to support businesses hit by mass staff absences and a wave of cancellations as Omicron hits.

A Treasury spokesperson highlighted ongoing support already in place, but appeared to hint that more help could be on its way, saying: “We will continue to respond proportionately to the changing path of the virus, as we have done since the start of the pandemic.”

Earlier, the head of the UK Health Security Agency, Jenny Harries, said the Omicron variant represented “probably the most significant threat” since the start of the pandemic. She told MPs on the Commons transport select committee to expect a “staggering” growth rate in cases over the coming days.

With new infections rising and the public being advised to take lateral flow tests before attending crowded events or visiting elderly relatives, UKHSA announced that it was doubling the number of test kits it could send out. With the help of Royal Mail, it will be able to dispatch 900,000 kits a day from Saturday, amid reports of some people struggling to order them.

Johnson is hoping to avoid taking fresh measures in the run-up to Christmas, after he was forced to rely on Labour votes to pass the government’s “plan B” restrictions, including the mandatory use of Covid passes for the largest venues.

The Independent Sage group of experts called for a 10-day “circuit breaker” before Christmas to stem the rapid rise of the Omicron variant, noting between now and 25 December there could be five doublings of cases at its current growth rate, meaning the situation could potentially be 32 times worse by then.

Among the measures they call for are the closure of indoor hospitality and entertainment venues, and no indoor gatherings between households of any size unless households are in bubbles.

“The opportunity for early action has been lost and the time for further delay is over. The situation is so urgent we must take emergency action now and that means it is imperative to reduce contacts. Advice is no longer enough since it does not convey the urgency of the situation,” they wrote.

Matthew Taylor, the chief executive of the NHS Confederation, which represents the healthcare system in England, Wales and Northern Ireland, warned that the NHS was already being hit by “increasing” numbers of staff falling ill with Covid.

Taylor urged the public to exercise “extreme caution” to help reduce the risk of the NHS being unable to treat their friends and family.