The latest Office for National Statistics (ONS) figures for 2021 show 624,828 live births in the two countries.
Of these, 320,713 (51.3%) were unregistered in women to marry or in a civil partnership.
The percentage of registered births to cohabiting parents has also increased compared to a decade earlier.
In 2021, mothers aged 30 and over were almost twice as likely to be married or in a civil partnership (60.5%) as mothers under 20 (31.2%).
The median age of mothers giving birth in 2021 rose to 30.9 years from 30.7 years last year, according to the ONS.
The average age of the fathers remained at 33.7 years.
The ONS said 2021 is the first year that the number of live births registered outside of marriage or civil unions has exceeded those registered in them since records began in 1845.
It follows a long-term trend of falling marriage rates and rising numbers of cohabiting couples seen in recent decades, the ONS added.
Because the full impact of the pandemic on marriage and civil union statistics is yet to be known, the Bureau of Statistics said caution should be exercised when interpreting its latest figures.
36.5% of all births were reported to cohabiting parents, compared to 31.2% in 2011.
The most popular day for the birth of babies was September 27 and the December 26th was the least popular.
stillbirths were most common in women aged 40 and over, at a rate of 5.9 per 1,000 births, according to the ONS.
It is followed by women under 20 with 5.0 stillbirths per 1,000 births.
A stillbirth is a baby born at 24 weeks or more who is not breathing or showing signs of life, the ONS said.
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The highest stillbirth rate was among black babies, at 6.9 per 1,000 births.
Stillbirths remain more common in the most deprived areas, the ONS said, adding that rates for mothers living in those areas have been consistently higher since 2015.
The stillbirth rate in the 10% most deprived areas in England was 5.6 stillbirths per 1,000 births, compared with 2.7 per 1,000 births in the 10% least deprived areas.
The most popular birth date in 2021 was September 23rd, the rarest December 26th.
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