The "no" vote creates challenges for National Air Traffic Services (Nats) management as it seeks to minimise disruption for airlines and passengers, while preparing to go live with the Swanwick centre's much-delayed systems.
The problems highlight some of the resourcing issues faced by senior managers when they take employees off normal duties to train on new systems.
Controllers had been offered £800 a day, for a maximum of 10 days, if they worked at London's ageing Air Traffic Control Centre near Heathrow instead of taking holiday or days off in lieu.
The aim of the "leave buy-back" was to provide reserves of controllers in London while employees were taken off normal operations to train on the computer systems at Swanwick, more than 40 miles away.
Without this contingency, Nats said it cannot guarantee a normal service if there are staff shortages caused by unusually high levels of sickness or leave.
Managers fear they may have to close a sector if there are too few controllers. Although this would not affect safety, it could cause delays if it happened during peak periods.
In a ballot involving members of the Institution of Professionals, Managers and Specialists, which represents nearly all air traffic controllers, 98% rejected the leave buy-back offer.
Some controllers said the result is a protest against the enthusiasm of senior Nats managers for the pending public private partnership. Others said staff are voting to protect their days off, which are particularly important in the light of the stress and pressure of their jobs. The union has warned that there is a serious shortage of controllers.
Nats said it was "disappointed" but added that the ballot result will not affect scheduled plans for training on Swanwick's new systems.
"We will now be talking to the union and staff representatives about how we can ensure sufficient cover," said a Nats spokesman.