The Deputy Mayor Councillor Tracey Baker with the Mayor Councillor Billy Blanchard-Cooper
The correct description on letters and envelopes is - The Deputy Mayor of Littlehampton, Councillor and their first and last name or more simply "The Deputy Mayor". If the Deputy Mayor is present without the Mayor and is representing him / her then he / she has the same precedence as the Mayor would have if he / she were present.
In speeches, one would say "We are pleased to have with us, The Deputy Mayor of Littlehampton, Councillor and their first and last name". At the commencement of the speech he / she would be referred to as Deputy Mayor though later in the speech for simplicity he / she could be referred to as Deputy.
If both the Mayor and Deputy Mayor are present the Deputy ranks immediately after the Mayor.
See our past Mayors