The Information Commissioner's Office (ICO) said the site was taking advantage of devices like CCTV cameras and remote-access baby monitors without security protection and with weak passwords.
"I want the Russians to take this down straight away," Christopher Graham, the information commissioner, told BBC Radio 4's Today programme.
"We've known about this for about 24 hours but we've been working out how best to deal with it because we want to take regulatory action," he said.
Britain is now planning "very prompt action" with the Federal Trade Commission, the US consumer protection agency, "to get this thing closed down", Graham said without giving further details.
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Roskomnadzor, the Russian communications agency, declined immediate comment.
In Britain, the ICO said around 500 feeds had been targeted, including a gym in Manchester, a house in Birmingham, and an office in Leicester.
"The website, which is based in Russia, accesses the information by using the default login credentials, which are freely available online, for thousands of cameras," said Simon Rice, ICO group manager for technology.
The site reveals the location and manufacturer of the device whose feeds have been accessed using software and search tools.
Chinese company Foscam was the most commonly listed manufacturer, followed by US firm Linksys and Japanese multinational Panasonic.