Defence Secretary Gavin Williamson said: "We take the security of our bases and personnel incredibly seriously.
"If a member of the public sees anyone acting suspiciously in or around a military base it should be reported to the police as a matter of urgency."
The news comes amid heightened political tensions between the UK and Russia after Moscow's GRU military intelligence agency was blamed for the poisoning of former spy Sergei Skripal and his daughter Yulia in Salisbury.