Yes you should be able to change the rate back, especially as it was initially introduced in error. The employees would have been able to eventually try and argue that this rate had become an implied contractual term through custom and practice.
There is a principle in employment law where terms may become implied into an employment contract by ‘custom and practice’. This makes them contractually binding even if they are not written down anywhere. This area of law is rather complex and it is usually only down to the courts to establish with certainty if something had become an implied term.
The basic requirement for implying terms is the presumed intention of the parties, in other words - did the employer and employee intend for the terms in question to be treated as contractual. In general, a practice would need to have been clearly communicated and consistently applied for a substantial period of time before it can be considered an implied contractual term. Therefore, something that is uncertain, not communicated properly, not been applied consistently or has just been around for a few months is unlikely to qualify.
So if this has only been in place for 13 weeks, was not properly communicated to them and was corrected as soon as the error was spotted it is unlikely they can try and argue it had become a contractual term.
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