Even with no new migration, Muslims are projected to increase as a share of Europe's population.
www.pewresearch.org
Relatively few recent immigrants to the UK (60,000) were refugees, but more than 1.5 million regular migrants arrived there in recent years. Overall, an estimated 43% of all migrants to the UK between mid-2010 and mid-2016 were Muslims.
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Not sure about that, either, since less than half of immigrants between 2010-16 were actually Muslim.
Conflating an immigration issue entirely with Islam doesn't help these people make their point. It undermines it.
The top 5 countries for UK migration are: Ireland, India, Pakistan, Romania and Poland.
Only one of those countries is majority Muslim, and immigration from Pakistan has been happening since the 50's.