A local resident told the BBC she alerted the police to suspicious activity near the base early on Sunday.
The woman, who did not want to be named, said she initially called the Ministry of Defence (MoD) police but nobody answered, and then called 999. She said she had seen three parked vans and a group of men wearing masks.
The MoD declined to comment.
Several residents said they had been led from their homes in the early hours and evacuated to a leisure centre.
Julian Tudsbury said he was woken up at 07:00 by police banging on his door in Whelford, where 85 households were advised to evacuate.
“There were several police, three police cars in the drive, and they said you need to evacuate, there’s been a major incident, said he couldn’t elaborate,” he said.
He said another local had seen three vehicles making their way to the base and called the police “straight away”.