Use an incorrect rating in association with their business, or to advertise that they have a particular rating when, in fact, they do not.
To do so i.e. displaying a 5 or a 4 when they are in fact a lower score on the Food Hygiene Rating Scheme constitutes a misleading action under regulation 5 of the Consumer Protection from Unfair Trading Regulations. This is a criminal offence.
In addition to this: once the offence has been highlighted and the food business operator has been made aware of the offence: failure to correct the rating may constitute a community infringement as defined by section 211 of the Enterprise Act 2002.
Trading Standards Authorities have powers to:
Take formal action under Part 8 Section 215 of the Enterprise Act 2002, and
To seek an Enforcement Order either at the High Court or County Court.
Such an Order would require you not to continue or repeat any conduct which constitutes a community infringement and can be issued personally against any controlling mind of the company.