Not every Mauritius Citizen does. However, since it is a a Republic within the Commonwealth, it is possible if there is a direct connection to the UK.
The following is from the UKBA website:
http://ukba.homeoffice.gov.uk/britishci ... hcitizens/
If you are not a British citizen, you may still have the right of abode if, on 31 December 1982, you were:
* a Commonwealth citizen with a parent who, at the time of your birth or legal adoption, was a citizen of the United Kingdom and Colonies because he/she was born in the United Kingdom; or
* a female Commonwealth citizen who was, or had been, married to a man who had the right of abode. You must have been married to him before 1 January 1983.
Hope this helps. Cheers!