The United Kingdom saw another day of rising coronavirus cases, deaths and hospitalizations, according to the British government.

The nation recorded 54,940 new cases Sunday, bringing the total number of cases to 3,072,349, the health data showed. The seven-day average for new cases rose from 21,698 on Dec. 10 to 61,106 on Jan. 1, the British government said.

The U.K. saw 563 new COVID-19-related fatalities Sunday, according to the health data. The country has 81,431 total deaths since the start of the pandemic, the government said.

There are currently 32,294 people hospitalized in Britain. The seven-day average for new hospital admissions rose from 1,728 on Dec. 10 to 3,345 on Jan. 1, officials said.

UK Health Secretary Matt Hancock confirmed on Sunday morning that every adult in the United Kingdom will be offered the coronavirus vaccine by the fall. 

Speaking on The Andrew Marr Show on BBC, Hancock said that the vaccine will be distributed according to need and that the British government has over 350 million doses of the vaccine on order.

"We are going to have enough to be able to offer a vaccine to everyone over the age of 18 and by the autumn," Hancock said in the interview.

Hancock also said that the priority is to immunize the most vulnerable 13 million people in the country by the middle of February -- something he confirmed to Sky News on Sunday that the U.K. government was on track to accomplish.

New numbers from The COVID Tracking Project are showing the dire situation facing the country right now, especially in the West.

There were just shy of 700 deaths reported in California on Saturday, with the state now averaging 410 death per day over the last seven days. The seven-day average for cases is up in 38 states since last week, including most states in the West, according to The COVID Tracking Project. In addition to the pandemic ravaging California, Montana and Washington have the second- and third-highest increases, respectively.

There were more deaths, cases and average hospitalizations this past week than any other during the pandemic, according to the project.

The report released Saturday showed a record seven-day average for total hospitalizations (130,350) and daily deaths (3,091). There were 3,500 deaths nationwide reported on Saturday.

The record-setting COVID-19 numbers continue to skyrocket in Los Angeles County.

The county crossed 900,000 confirmed cases on Saturday -- more than twice as many as any other county in the nation. There were also another 221 deaths reported Saturday, bringing the total to 12,084. Sixty-five of the people who were reported dead on Saturday were 30 to 64 years old, the remaining were older. LA County alone has more total deaths than 41 U.S. states.

There are currently 7,966 people hospitalized with coronavirus in the county, 22% of whom are in the intensive care unit.

"To the families and friends experiencing the sorrow of losing of a loved one due to COVID-19, we send you our deepest condolences," Dr. Barbara Ferrer, the county's health director, said in a statement. "This is another devastating day for Los Angeles County. The speed with which we are reaching grim milestones of COVID-19 deaths and cases is a devastating reflection of the immense spread that is occurring across the county. And this accelerated spread reflects the many unsafe actions individuals took over the holidays."

Of the 4.96 million people tested so far in the county, 17% have tested positive.

ABC News' Bonnie McLean contributed to this report.