Mr Yezhov is said to have accompanied Ukrainian PM Volodymyr Groysman on a visit, and was photographed with his boss and Mrs May in Number 10.
The detained man turned out to be Stanislav Yezhov who served as the deputy head of the protocol for the Prime Minister Volodymyr Groysman.
The arrest is embarrassing for the Ukrainian authorities.
The Ukrainian press has found out that Yezhov's wife is a citizen of Russian Federation, graduated from Saint Petersburg University and works at the Kiev-based Donbass Fuel and Energy Company. He was detained, ' Groysman said on Facebook.
Interior Minister Anton Gerashchenko said Mr Yezhov had "worked for the Russian special services for at least two years".More news: Iranian prisoner Nazanin Zaghari-Ratcliffe 'could be released in weeks'
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In June 2016 he visited the White House and interpreted for Groysman during a meeting with the then United States vice-president, Joe Biden. It supplied him with "special equipment" which was used to collect information about the "activities of [Ukrainian] government structures". "The intruder transferred the collected data via electronic communication channels", the press office of the Security Council reported.
A spokesman said: "We've read news but we have no information".
The SBU said in a statement that Russian intelligence had recruited Yezhov during a "long-term foreign mission".
The revelation came as Foreign Secretary Boris Johnson travelled to Moscow for a meeting with Russian counterpart Sergey Lavrov tomorrow.
'We have agreed today to bolster our cooperation to counter Russian disinformation in the region. we are both deeply concerned by Russia's attempts to weaponise information, ' she told reporters during a visit to Poland. It is not our practice to comment on legal proceedings in other jurisdictions'.