They are probably right: global birth rates by religion (via quick google search)
Muslims: Have the highest fertility rate, averaging 3.1 children per woman in a 2010-2015 study.
Christians: Have the second-highest rate, at an average of 2.7 children per woman.
Hindus: Have a fertility rate of 2.4, similar to the global average.
Buddhists: Have a fertility rate of 1.6 children per woman.
Religiously unaffiliated: Have a low fertility rate of 1.7 children per woman.
The birthrate for England and Wales was 1.4 children per woman in 2024. That number does not separate Muslims from Christians or others descended from the native population of England and Wales. No trend is immutable but if it does not change, Britain will be a Muslim caliphate, as will France, Germany, Belgium, the Netherlands, Ireland, Denmark, Norway, and Sweden, within a century or sooner, maybe much sooner.