Dame Caroline Dinenage, chair of the House of Commons Culture, Media and Sport Committee, wrote to Rumble to say she was "concerned" that Brand could profit from the host of content he posts.
Rumble is a site that attracts creators who tend to subscribe to more right-wing views.
The letter follows claims of rape, sexual assault, and emotional abuse from four women against Brand, prompting YouTube to demonetise his videos, as well as internal investigations by his ex-employers, including Channel 4 and the BBC.
Several other companies have cut ties with the comedian, but Rumble said it will not be doing so. The firm branded the letter from Dame Caroline "disturbing," writing in a statement that it will refuse to "join a cancel culture mob".
Brand currently has 1.4 million followers on Rumble, where he posted a daily show until the claims emerged.
He used the site to send out a pre-emptive response to the accusations - all of which he denies - by The Sunday Times and Channel 4's Dispatches.
Rumble's statement on X, formerly Twitter, said: "Today, we received an extremely disturbing letter from a committee chair in the UK Parliament.
"While Rumble obviously deplores sexual assault, rape, and all serious crimes, and believes that both alleged victims and the accused are entitled to a full and serious investigation, it is vital to note that recent allegations against Russell Brand have nothing to do with content on Rumble's platform.
"We regard it as deeply inappropriate and dangerous that the UK Parliament would attempt to control who is allowed to speak on our platform or to earn a living from doing so.
The statement finishes: "Although it may be politically and socially easier for Rumble to join a cancel culture mob, doing so would be a violation of our company's values and mission. We emphatically reject the UK Parliament's demands."
It also criticises the choice of YouTube to demonetise Brand's channel "based solely on these media accusations".
Dame Caroline had written to ask about whether Brand could make money from his content, and what Rumble is doing to ensure that creators are unable to use the site to "undermine the welfare of victims of inappropriate and potentially illegal behaviour."
Brand has been accused of rape, assault and emotional abuse between 2006 and 2013, when he was at the height of his fame.
Channel 4 chief executive Alex Mahon addressed the allegations on Wednesday, labelling them "disgusting and saddening".
The BBC has also announced a review into Brand’s time at the corporation between 2006 and 2008 which director-general Tim Davie said will have an “initial report in weeks, not months”.
During a long-arranged session with BBC staff on Tuesday, he said the probe will be led by the BBC’s director of editorial complaints Peter Johnston and “the objective is to be totally transparent”.
The news comes after the remaining shows of Brand’s Bipolarisation tour were postponed and the Metropolitan Police said it had received a report of an alleged sexual assault in Soho in 2003.
One of the alleged victims, under the pseudonym Alice, said that Brand sexually assaulted when she was 16 and he was 30, and that he used a BBC car to ferry her to and from his London flat.
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