Britain's media regulator says it is considering an official letter received from Iran's embassy in London complaining about media coverage of the protests.
The regulator, known as Ofcom, said on Friday the letter is being carefully evaluated.
Iranian state media say the government is complaining about what it calls a propaganda campaign orchestrated by UK-based Persian-language broadcasters.
The letter asserts that the media outlets violated UK and international media regulations and tried to incite protesters into using violent tactics.
Ofcom has a broad regulatory role in Britain, overseeing television, radio, high-speed internet and other sectors. One of its roles is to protect British consumers from harmful content.
Protests began on Thursday in the north-eastern city of Mashhad, with anti-government rallies quickly spreading to other cities including Tehran, Khorramabad, Karaj and Sabzevar.
Thousands are thought to have taken part in the protests, making them the biggest show of public defiance since 2009, when Iranians - as part of the newly-formed Green Movement - took to the streets to denounce alleged rigged presidential elections by then-President Mahmoud Ahmedinejad.
The protests this time were initially centred around rising living costs, but quickly became focused against the regime in general with chants of "Death to the dictator".
In an attempt to shut down protests and manage the unrest, Iran's government blocked access to the encrypted Telegram messaging app and the photo-sharing app Instagram, which now join Facebook and Twitter in being banned.
A total of 21 people have so far died since protests began and some 450 have been arrested since Saturday, December 30.