The chain says an independent audit has been launched.
BBC reports that 26 employees of Costa Coffee franchise stores managed by Goldex Essex Investments Ltd and Bristal Investments Ltd have complained against management on alleged refusal to pay for sickness or annual leave, working outside of contracted hours and the retention of tips.
The latest allegations surfaced after reports that staff at Costa stores managed by Kafeel Khan's Goldex Essex Investments Ltd were being charged a minimum of £200 for their own training.
A Costa Coffee spokeswoman told BBC that an independent audit has been launched.
"Given the serious nature of the allegations, we have today informed all of our Individual Franchise Partners that we will be launching an independent audit into the legal and ethical compliance of their operations, including employment matters," she said.
The audit also comes after the coffee chain announced that Dayforce will manage their recruitment, HR and payroll processes as part of a wider people management technology transformation initiative.
The retailer also plans to implement Dayforce Payroll, which combines payroll and time in one system, ensuring that employees are paid accurately and on time with built-in support for UK-specific requirements.
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