Liberal Democrat MP Tom Gordon and 53 other parliamentarians have written to Culture Secretary Lisa Nandy, warning her Masha and the Bear features militaristic themes.
They were joined in signing the letter by three members of Ukraine's parliament Yevheniia Kravchuk, Halyna Vasylchenko and Kira Rudyk.
Gordon told the Press Association that, after being frozen out of several international forums over recent years such as the then-G8 and Eurovision Song Contest, Russia might be using exports such as Masha and the Bear to return to the world stage.
Asked whether the government should sanction the TV show, he said: "If people have breached international law, then perhaps we shouldn't be giving them a platform."
In a statement to The Guardian, a spokesperson for the studio behind Masha and the Bear denied it featured Russian propaganda.
Masha and the Bear was launched in Russia more than 17 years ago and has now racked up billions of views worldwide.
In the cartoon, best friends Masha, a little girl, and a large brown bear embark on adventures around the world and occasionally in space.
One episode, titled Recipe for Disaster and uploaded by the user Get Movies, has garnered more than 4.6 billion views on YouTube.
The Kyiv-based Centre for Countering Disinformation has previously warned the cartoon promotes "a positive image of Russia, in the form of a large, good-natured bear".
It also promotes "normalisation of the Soviet past and military symbols in children's environments," the organisation claimed.
It alleged the program's studio Animaccord, which is based in Limassol, Cyprus, but has previously had an office in Moscow, maintains direct ties to Russia through its owners and intellectual property rights.
In their letter this week, the MPs pointed to a post on Masha and the Bear's English-language X account from 2015 as an example of propaganda.
Masha appears wearing a large green military-style hat with a red star in the centre, with the accompanying text: "Woo hoo, I'm in the army now!"
It is captioned: "A real army girl with a butterfly net."
The MPs described the hat as "the cap of an NKVD border guard, an agency responsible for mass deportations, executions and the persecution of tens of millions of people".
They added: "British children watching this program on Netflix or ITVX are part of an audience potentially generating revenue for a studio that is, in effect, helping to finance Russia's war machine.
"The propaganda content is not subtle."
ITVX declined to comment.
The broadcaster is not thought to have spent large sums to carry Masha and the Bear on its platforms and its contract is with a business registered in Cyprus.
Animaccord spokeswoman Melanie Bonvicino told The Guardian: "My client categorically rejects the false and defamatory suggestion that Masha and the Bear is associated with propaganda".
She added that "Animaccord operates in full compliance with applicable laws" and "the series contains no political messaging, and any claim to the contrary is wholly unsupported by its content".
