Yes. You must always carry out a Right to Work Check, even if the person is a British citizen.
You must not make assumptions about anyone’s eligibility to work in the UK based on:
Nationality
Appearance
Accent
Any other personal characteristic
How a British citizen can prove their Right to Work
A British citizen can demonstrate their eligibility to work in the UK by providing an appropriate document, such as:
A valid UK passport
You should:
Check the document carefully
Confirm it is genuine, valid, and belongs to the person
Record and retain a copy, in line with Right to Work guidance and your internal policies