Story highlights Kremlin spokesman rejects MI5 chief's claims

MI5 director-general also says "there will be" terrorist attacks in the UK

London (CNN) Britain faces a growing threat from covert attempts at destabilization by Russia, the head of the country's security and counter-intelligence agency MI5 has said.

In an interview with The Guardian newspaper published Tuesday , Andrew Parker, director-general of MI5, said that the covert threat from foreign countries, most notably Russia, was rising at a time when the threat of radical Islam drew the most attention.

Russia was "using its whole range of state organs and powers to push its foreign policy abroad in increasingly aggressive ways -- involving propaganda, espionage, subversion and cyber attacks," he said, in the first newspaper interview with an incumbent MI5 chief in the service's history.

"Russia is at work across Europe and in the UK today. It is MI5's job to get in the way of that."

Besides Russia's high-profile activities in Ukraine and Syria, it was also responsible for "high-volume activity out of sight with the cyber-threat," he said.

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