Britain recorded 1,035 new deaths from COVID-19 on Saturday (local time), down from Friday's record toll of 1,325.
It marked the fourth consecutive daily toll - defined as deaths within 28 days of a positive COVID-19 test - of above 1,000.
The government figures also showed 59,937 new cases, down from 68,053 the previous day.
Meanwhile in Ireland, health officials said on Saturday (local time) that three cases of a new coronavirus variant found in South Africa are believed to be contained.
Ireland is currently grappling with a COVID-19 surge that exceeded the first wave last year. On Friday, the country confirmed its first cases of the more infectious variant in people who had travelled to Ireland from South Africa over the Christmas holidays.
This week, Ireland reported an increasing presence of the variant first found in England. It was detected in 25 percent of positive cases that underwent further testing in the week to January 3, up from just 9 percent two weeks earlier.
"The UK variant is of more concern to us purely because of the amount of virus that's on the island, and we know that it's transmitting in the community," Cillian De Gascun, the head of Ireland's national virus laboratory, told national broadcaster RTE.
"The good thing about the South African variant is we know exactly where those cases came from, they have been contained, controlled and contact traced, and to the best of my knowledge there was no onward transmission."
The government announced its strictest lockdown measures since early last year on Wednesday (local time), warning that a "tsunami" of infections fuelled by the UK variant and the relaxation of curbs ahead of Christmas could overwhelm the healthcare system.
The number of patients in Irish hospitals with COVID-19 rose by 12 percent in the space of 24 hours on Saturday to 1,285, having in recent days exceeded the peak of 881 set during the first wave of infections.
Fourteen more patients were admitted to intensive care units (ICU). That brought the total number receiving critical care to 119 and left just 27 of the 284 ICU beds in the country's public hospitals empty.
Those hospitals can increase ICU capacity safely to 375, the head of Ireland Health Service Executive (HSE) said this week. The HSE has also reached an agreement to take over private hospital ICU beds for COVID-19 admissions.