The move is a part of a crackdown on anti-social behaviour by the council.
Anyone spotted wearing face coverings to hide their identity and cause harassment can be stopped.
The new rule excludes religious head coverings but also extends to aggressive begging.
The move follows a consultation with residents that showed strong support for action on anti-social behaviour in the borough. The Council survey found:
83% of respondents wanted to see the new rules introduced
80% of residents had experienced these behaviours in the last year
40% said they were affected by them on a daily or weekly basis.
