No, it is quite uncommon. I have never met or heard of a real person with this name.
However, it sounds very English.
George Twisleton was born in 1618.
George Twisleton died in 1667.
Francis Morphet Twisleton was born in 1873.
Francis Morphet Twisleton died in 1917.
Edward Turner Boyd Twisleton has written: 'Evidence as to the religious working of the common schools in the state of Massachusetts, with a pref' -- subject(s): Church and education
According to The British Surnames Website, the third most common surname is "Harris". (see related link)
Jackson is a Scots and English surname meaning "son of Jack" and is very common in all parts of the British Isles.
The most common South American surname in Argentina is Fernandez. In Brazil, the most common surname is Silva. In Chile, the most common surname is Gonzalez.
Most people in the United Kingdom is Smith. The most common name for a British woman is Anne Smith and the most common name for a British man is David Jones.
Garcia is the most common surname in Spain.
Garcia is the most common Spanish surname.
The most common surname in Greece is Papadopoulos.