The train operator would say only that it would be able to run "the majority of services" during any strikes or other industrial action.
The company runs most trains between Glasgow and London, and also operates between Edinburgh and London via Birmingham.
The RMT said its members had voted by more than nine to one to strike over "pay justice" with train drivers.
Among nearly 1,500 workers taking part in the ballot were train managers (guards), and catering, station and office staff.
An RMT spokesperson said: "At the heart of the dispute is the RMT demand for a suitable equal offer for its Virgin West Coast members to that received by drivers.
"Virgin have agreed a deal for drivers to buy out their claim for a one-hour reduction in the base working week without loss of pay by giving an additional Â£500 on their basic salary, which is pensionable, whilst asking RMT to enter into self-financing arrangements for other grades."
General secretary Mick Cash said: “Our members have voted overwhelmingly for action in this ballot which is all about workplace equality and workplace justice.
“The result will now be considered by the union’s executive and we remain available for serious talks aimed at righting this wrong.”A spokesperson for Virgin Trains said: “We are disappointed by the result of the RMT’s ballot, but can reassure customers that we will be able to run the majority of services during any industrial action.
"We have offered a 3.2 per cent annual pay increase at a time when the average increase across public and private sector employees is around 2 per cent.
"We remain open to continuing talks with the RMT."