Under the model which assumes median migration levels, the number of Muslims in the country would rise from 4.1m in 2016 to 13m in 2050.
The US-based think tank says that the UK has been the major destination for economic migrants coming to Europe, while Germany has been the top destination for refugees.
It said the research followed a “record influx of asylum seekers fleeing conflicts in Syria and other predominantly Muslim countries”.
The UK also has one of the largest gaps in fertility rates between Muslims and non-Muslims, with Muslim women having an average of 2.9 children compared to the 1.8 had by non-Muslims.
This means that even if migration were to stop completely, the group’s population share would rise by more than 3 percent in the UK, as well as in France, Italy, and Belgium.
The paper suggests that if migration continues at the same rate but refugee movement stops, the UK will have the highest overall population of Muslims in the EU, at 13m, making up 16.7 percent of the population.
Currently, the country is behind Germany and France in the overall population of Muslims.
“Overall, an estimated 43 percent of all migrants to the UK between mid-2010 and mid-2016 were Muslims,” the paper said.
The study also shows that the UK has one of the lower levels of hostility toward refugees from Iraq and Syria.
Just over one in three people see them as a major threat, compared to 39 percent in France, 42 percent in Spain and 60 percent in Poland.
It concluded that people in countries with lower overall numbers of refugees were more likely to believe they were a threat.
According to figures from the Oxford-based Migration Observatory, one in five non-UK born people in the UK is Muslim.