Sutyagin, who served 11 years in prisons, has maintained his innocence Two of the four Russians expelled from Moscow in a spy swap are reported to be staying undercover in a British hotel.
The brother of one, Igor Sutyagin, said he had called his wife from a small town on the edge of London, but had not been told exactly where he was.
The four US spies were swapped for 10 Russian agents who admitted in the US to being agents for a foreign country.
Meanwhile Britain is "urgently reviewing" whether to deprive Russian spy Anna Chapman of her UK passport.
Last week her lawyer said she would like to come to the UK as she has a passport through her former marriage.
The spy swap was carried out in Vienna last week, after which it was reported that two of the four US spies were flown to England.
BBC diplomatic correspondent James Robbins said the two, who were convicted of spying for the West, were apparently being supervised by British minders who were "clearly keen to keep their location secret".
Mr Sutyagin had called his wife in Russia, telling her he was in a small town on the outskirts of London but hadn't been told anything more, according to his brother Dmitry.
Mr Sutyagin was apparently given an untraceable telephone calling card to make the call.
Anna Chapman worked in London's financial sector for several years His brother added he was hoping he would be given a British visa while he considered what to do next. British connections were alleged by Russian prosecutors at the trials of at least two of the men, including Mr Sutyagin.
He was convicted of passing information about submarine and missile systems to a UK firm allegedly used as a front by the CIA.
The nuclear specialist had served 11 years of a 15-year sentence in the Arkhangelsk region of northern Russia when he was included in the spy swap. He has always maintained his innocence.
A second man, Sergei Skripal, was convicted of passing the identities of Russian intelligence agents working undercover in Europe to the UK's Secret Intelligence Service (commonly known as MI6).
British husband Ms Chapman, 28, worked in the financial sector for a few years after moving to London in 2002.
Earlier this month Briton Alex Chapman, 30, from Bournemouth, Dorset, talked to a newspaper about his four-year marriage to the Russian.
He said they had met at a party in London in 2002 and married five months later.
Following the spy swap a UK Home Office spokesperson said they were reviewing Ms Chapman's passport situation.
"The home secretary has the right to deprive dual nationals of their British citizenship where she considers that to do so would be conducive to the public good. This case is under urgent consideration," they said.
Shadow Home Secretary Alan Johnson said it "cannot be in our interests" to let her settle in the UK.
'Four good ones' The 10 Russian agents had pleaded guilty in New York to "conspiracy to act as an unregistered agent of a foreign country".
More serious money-laundering charges against them were dropped.
Prosecutors said the accused had posed as ordinary citizens, some living together as couples for years, and were ordered by Russia's External Intelligence Service (SVR) to infiltrate policy-making circles and collect information.
Meanwhile, in the US, Vice President Joe Biden has been defending the spy swap.
He told a television chat show: "We got back four really good ones, and the 10, they've been here a long time, but they hadn't done much."
BBC
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