An intelligence source claims foreign agents are using “Cold War tactics” to target the British negotiating team.
Email accounts and mobile phones are believed to have been hacked by overseas governments.
Some countries are using honey-trap operations, where beautiful women seduce officials in the hope of extracting secrets.
It is believed EU negotiators enlisted spies to discover the weaknesses in Britain’s negotiating strategy.
Offices are now routinely checked for bugs, while phones and laptops are scanned for software planted by foreign agents, a senior source told this newspaper.
The insider said “nothing was off limits” and EU spooks were using “every known espionage tactic” to learn our secrets.
The level of spying by so-called friendly nations has increased dramatically in recent weeks as Brexit talks reached crisis point.
Now officials are being urged to be extra vigilant and conduct daily counter-espionage drills.
They have also been warned important phone calls should only be made on mobiles which cannot be hacked.
It is also understood that GCHQ is monitoring foreign intelligence organisations so it can warn ministers of any potential threats.
The source said: “There have been incidents of files going missing and of email accounts and mobile phones being hacked.
“There is the possibility that rooms may be bugged or that conversations between British officials are being listened to using long-range microphones.
“The EU is deploying Cold War espionage tactics against Britain.
“And to be fair Britain is probably doing the same against the EU.”
France and Germany were said to be the main culprits but Polish and Lithuanian spies are involved too.
Our source added: “The French work very closely with the UK on counterterrorist operations but the gloves are off as far as Brexit is concerned.”