Last month the firm announced plans to relocate 370 staff from its bases in Bellshill, Uddingston, Renfrew and Swansea to a new facility run by SITEL UK in Strathclyde Business Park.
Existing staff will be subject to a TUPE with a 45-day consultation starting last month.
One staff member said: “Virgin has advised they are bringing more jobs to Scotland, although there will be more jobs, this is not directly for working for Virgin.
“Virgin has a TUPE agreement with SITEL, which is affecting staff from Lanarkshire. ACAS has advised we should not be negatively impacted, but this is possibly going to be the case.
“As we currently get great benefits and uplift on wages, and this may all be affected and may have a negative impact on staff.
“Everyone at Virgin loves their jobs, but we also want treated fairly.”
A Virgin Media spokesperson responded: “Our understanding from SITEL is that they will be honouring contractual employment terms of those transferring.
“Any changes to benefits and policies (which are non-contractual) which may be proposed by SITEL will be discussed during the consultation process.”