Well, sort of ...
The Soveriegn and members of the Royal Family do not exercise their right to vote. This applies to the Royal Highnesses, and not to the extended family. Viscount Linley and his sister, Lady Sarah Chatto, have been photographed at the polls in previous elections, and, they probably cast their votes in this election, too.
This self-imposed bar does not apply to Princess Anne's children, who are not royal highnesses.