At least one person in the UK has died with the Omicron coronavirus variant, the prime minister has said.
Boris Johnson said the new variant was also resulting in hospital admissions and the "best thing" people could do was get their booster jab.
Visiting a vaccination clinic in London, he said people should set aside the idea Omicron was a milder variant.
On Sunday, the PM set a new target for all adults in England to be offered a booster by the end of the month.
On Monday, Mr Johnson said people needed to recognise "the sheer pace at which [Omicron] accelerates through the population".
The NHS website crashed on Monday after more than 110,000 people tried to book their booster before 09:00 GMT, the government said.
There have also been long queues at walk-in centres and new orders for lateral flow tests on the government website have been temporarily suspended due to high demand.
The prime minister said there were still "ample supplies" of tests for people to collect from pharmacies.
From Tuesday, people who are fully vaccinated will be advised to take daily tests if they are identified as a contact of someone who has Covid.
Online bookings for boosters opened for over-30s on Monday, while 18 to 29-year-old will be able to book online from Wednesday. Over-18s can now also get their booster at some walk-in centres in England - as long as it has been three months since their second dose.
On Monday, the UK Health Security Agency confirmed 10 people had been admitted to hospital in England with the Omicron variant.
Their ages ranged from 18 to 85 years old and the majority had received two doses of a Covid vaccination, the agency said.
Around 70 Conservative MPs have signalled they could oppose some of the new measures in a Commons vote on Tuesday, particularly mandatory Covid passes.
However, Labour has said it will back the plans, so they will almost certainly be approved.
The prime minister has repeatedly declined to rule out further restrictions ahead of Christmas.
The prime minister visited a vaccination clinic in west London on Monday
The booster rollout has been accelerated in response to Omicron, after early analysis suggested two doses of a Covid vaccine were not enough to stop people catching the variant.
A third booster dose gives around 70% to 75% protection against symptomatic infection with Omicron, analysis by the UK Health Security Agency found.
Earlier, Health Secretary Sajid Javid said the UK was in a "race between the virus and the vaccine" and the NHS would be focusing on urgent appointments for a few weeks, with non-urgent treatment potentially delayed until the new year.
Data suggests Omicron is more transmissible than previous variants, with cases doubling in the UK every two to three days.
The UK's Covid alert level has been raised to level four - which means a high or rising level of transmission - for the first time since May due to the spread of Omicron.
To reach the government's boosters target, one million doses would have to be administered a day.
More than half a million booster jabs and third doses were given in the UK on Saturday, the second day that has happened since the booster rollout began.
Some 750 armed forces personnel have been made available to support the booster rollout in England and Scotland.
And England's deputy chief medical officer Prof Jonathan Van-Tam has written to everyone who previously volunteered to help the vaccine rollout to encourage them to return to help with the booster programme.
Scotland is also aiming to offer booster vaccine appointments to all over-18s by the end of the year, while Wales is trying to ramp up its rollout to meet the same target. In Northern Ireland, over-30s are now eligible for booster jabs.
The UK recorded 48,854 new coronavirus cases on Sunday, as well as 52 deaths within 28 days of a positive test.
BDST: 2038 HRS, DEC 13, 2021