Well, it is all due to the very nature of Islam being the original faith that Our Creator set forth for us to follow within our hearts.
For those who choose to use their God given intelligence and faculties of logic and reason, they would find the answer in many of Allah's Final and Complete Revelation to Mankind ~ the Holy Qur'an.
For example in Surah Adh-Dhariyat (The Winnowing Winds) Chapter 51 Verse 56, Allah Azza Wa Jalla says :

Transliteration
Wama khalaq tu al jinna wal-insa illa liya' budoonSahih International
And I did not create the Jinn and Mankind except to worship Me.From scientists to atheists, clergymen to those who were strongly Anti-Muslim extremists, large numbers of born British individuals are steadfastly and firmly living their life as committed practicing Muslims and turning Islam as the preferred form of faith in the UK.
Many good decent people who happen to be born into faiths such as Christianity, Hinduism, Buddhism, Sikhism, Taoism and many beliefs gradually realize that there is still something missing from their life.
They start to question their faith?
Why are they not achieving their peace of mind? Why is it that despite their years and years of devoting their life to their deities and gods which they have been worshiping since they were kids, there is still that emptiness in their heart. A feeling of desolation yearning for fulfillment within their soul.
Even those who have been in the service of the church and been dedicating their life as priests or nuns, gradually start to see that the answers to their many questions which have not been answered by the teachings of their born faith which is Christianity found the Truth of Al Islam.
Watch this video of a Catholic Church priest who found the answers in Islam share his journey to becoming a committed Muslim.
Witness the growing number of white British citizens who have become Muslim.
Those who study about Islam will come to understand that Allah, God Almighty has been sending His prophets and messengers to Mankind since the Creation of Our Father, the Prophet Adam Alaihis Salam with the same message which is to worship no other god but Allah!
Watch a Jewish professor admitting that all of God's prophets were Muslim :
This and many other examples are proof that Islam is our birthright and in the UK, the British are embracing Islam with a burning passion that can best be described by Surah An Nasr Chapter 110 Verses 1 to 3:

Transliteration
Izha jaa anasru Allah hiwal fathSahih International
When the victory of Allah has come and the conquest,
Transliteration
Wara aytaan nas sa yadh khuloo nafee deeni Allahi afwajaSahih International
And you see the people entering into the religion of Allah in multitudes,Alhamdulilah!
This was my small effort in sharing Islamic Information material with the visitors to our masjid. Sheikh Ahmed Deedat's Dakwah books and multimedia were my main selections given away for free and some were for sale.
May Islam fluorish all over the world and help bring some light to those seeking for the Truth.
Ameen.