The only way they'll get that sort of population expansion is if they enact very liberal immigration policies, which is not something most nations in Europe are signaling they're willing to do (quite the opposite so far).
That's enough to make the UK ~40% immigrant in one lifetime (80 years). Given how rare it is for countries to change so significantly so fast, it's fair to say that they already have very liberal immigration. The UK population rose from 63 million in 2011, to 68 million in 2023, despite a below-replacement fertility rate of 1.74 [1].
While it's true that most nations in Europe want lower immigration [2,3,4], such sentiments rarely translate into policy, similar to the US.
[1] https://en.wikipedia.org/wiki/United_Kingdom
[2] Europeans overwhelmingly against immigration: Poll (2011) - https://www.euractiv.com/section/social-europe-jobs/news/eur...
[3] Europeans Most Negative Toward Immigration (2015) - https://news.gallup.com/poll/186209/europeans-negative-towar...
[4] Poll reveals great unease among Europeans about migration policy (2022) - https://www.brusselsreport.eu/2022/02/01/poll-reveals-great-...