He added: “Our very weakness — as a result of Brexit, as a result of fraying trans-Atlantic ties — was an attraction for Russia. The weaker a country, the more attractive a target it is for bullies.”

Mr. Sawers, who headed the Secret Intelligence Service, known as MI6, from 2009 to 2014, also warned that by leaving the European Union, Britain would lose access to information-sharing mechanisms like passenger records and the Schengen Information System, slowing its ability to solve crimes and extradite suspects.

“The sort of thing Britain might lose access to is the ability to track terrorists around the E.U.,” he said in an interview. “It also loses the capacity to extradite suspects, including ordinary criminals and pedophiles. It takes days under the E.U. arrest warrant. It used to take months or years.”

He said that there was “real concern” in intelligence circles about losing access to these tools, but that it is not often aired publicly because “intelligence and security issues tend to be dealt with behind closed doors.”

Noting that Prime Minister Theresa May proposed a new treaty to preserve these arrangements, he asked, “Why are we leaving in the first place?”