The 28-tonne "battle bus" is thought to have been built in the 1980s for the former prime minister's Northern Ireland tour.
The vehicle was sold on Thursday night and beat the estimate of £10,000, selling for a final £16,940 to a vehicle collector, said Jonathan Humbert, of Northamptonshire-based JP Humbert Auctioneers.
"There was immense interest in the bus," he said. "It sold to a spontaneous round of applause in the saleroom."
The bus, which has just 17,398 miles on the clock, has a blast-proof floor and armour-plated glass throughout, as well as a bomb-proof armour-plated body.