What statisticians term 'natural' population growth - the difference between births and deaths - fell to just 400, the lowest since 1978, while net international migration rose to 622,000, up from 548,500 in the previous 12 months.
A net 13,800 people also moved from England and Wales to Scotland or Northern Ireland.
Britain's Office for National Statistics said the population increase in England and Wales was the largest since 1948, when a post-World War 2 baby boom and the return of British military personnel serving overseas caused a rise of 1.5 million.
The population for the whole United Kingdom was 67.6 million in mid 2022. Data for 2023 is not yet available.
Economic output has not kept up with the rising population. Based on provisional population figures, gross domestic product per head in 2023 was 0.7% lower than a year earlier.
Net migration to the United Kingdom hit a record 764,000 in 2022 and fell 10% to 685,000 in 2023, but is more than double its level in 2015, just before the Brexit referendum.
Reducing immigration was a key goal of many Britons who voted to leave the European Union.
Britain's previous Conservative government said it wanted to reduce net immigration, and Prime Minister Sir Keir Starmer's Labour Party pledged in the election campaign to do so too by making the economy less reliant on foreign workers.
Post-Brexit changes to visas sharply reduced the number of EU migrants to Britain, but new work visa rules led to a surge in immigration from India, Nigeria and Pakistan, often to fill health and social care vacancies.
At the end of last year the government tightened rules to stop low-paid social care workers from bringing dependents.
Meanwhile, Starmer recently confirmed his newly formed government would not pursue predecessor Rishi Sunak's policy to deport asylum seekers who arrive in small boats to Rwanda, ending the scheme before any flights took off.
"The Rwanda scheme was dead and buried before it started. It's never been a deterrent (to small boat crossings)," Starmer said at a news conference. "I'm not prepared to continue with gimmicks that don't act as a deterrent."
