Staff were informed of the move on Tuesday (July 3).
The airline says it will consolidate its contact centre operations at a single base in Swansea.
A Virgin Atlantic spokesperson told TTG around 150 people were affected by the proposed changes and a "period of consultation" was under way for them to discuss their options.
TTG though understands a number of members of staff have either already voluntarily taken redundancy, or have been made redundant.
The spokesperson added: “We’re committed to providing our customers with the most personalised service of any UK airline, and currently have two contact centres based in Crawley and Swansea.
“The way our customers engage with us is changing, and in order to continue to offer unrivalled service to our customers we plan to bring our contact centres together at a single site in Swansea.
“Being located together will make it easier to roll out the digital enhancements our customers expect, and operate a large 24/7 contact centre operation.
“We are really proud of our loyal and dedicated contact centre team and are focused on supporting people impacted by this change.”
Virgin Atlantic employs around 9,000 people in the UK.
Its Crawley site is the airline’s main training centre for crew, contact centre and engineering staff.
