According to Tree Guide UK: "The Turkish Hazel Corylus colurna, native to South-East Europe, Turkey and Iran was introduced to Britain in 1582"
https://www.treeguideuk.co.uk/...
So it is not native to the UK as it was introduced from elsewhere. From another reference, while it is widely planted, for example as a street tree or in parks, it is rare to find a naturalized one (one that has spread naturally from an introduced plant).
https://www.naturespot.org.uk/...
