"Nobody wants to tell the stars what they should or shouldn't say and bosses expect the odd reference, but the last thing they want is a string of political rants - particularly with Trump's UK visit and his Muslim ban in full flow."
The Sun also reported that the BBC will make edits to the event, which is broadcast on a two-hour delay, if winners "talk about racism".
Last weekend's SAG Awards saw several actors criticise the Trump administration, while Stranger Things star David Harbour pledged to "punch some people in the face when they seek to destroy the weak, the disenfranchised, and the marginalized."
"My father fled religious persecution in Nazi-occupied France," added Veep star Julia Louis-Dreyfus in her acceptance speech. "I'm an American patriot and I love this country, and because I love this country I am horrified by its blemishes. This immigrant ban is a blemish and it is un-American."
Supporting Actor winner Mahershala Ali referenced his conversion to Islam, and spoke about collective embracing of people's differences.
"When we kind of get caught up in the minutiae, the details that make us different, there's two ways of seeing that," the Moonlight star said. "There's an opportunity to see the texture of that person, the characteristics that make them unique. And then there's the opportunity to go to war about it - to say, 'That person is different from me, and I don't like you, so let's battle.'"
Actress Sarah Paulson also urged fellow industry figures along with the viewing public to donate to the American Civil Liberties Union, a non-partisan, non-profit organisation designed to defend and preserve the individual rights and liberties of residents of the United States.
Emma Stone, Lily Tomlin, Ashton Kutcher and Taraji P. Henson also made politically-themed speeches at the ceremony.
Meanwhile, at the Golden Globes in January, Meryl Streep condemned Trump's politics and his impersonation of a disabled journalist.
"This instinct to humiliate, when it's modelled by someone in the public platform, by someone powerful; it filters down into everybody's life because it kind of gives permission for other people to do the same thing," she said.
The BBC told The Sun in response to the article that it aims to fairly and accurately reflect award-winners "passionately held views".
In a statement, the BBC said: "All content on the BBC is published in line with our editorial guidelines. As with any televised awards show, we seek to fairly and accurately reflect the passionately held views of recipients and attendees.
"At the same time, we have a duty to fairly reflect as many awards, nominees and winners as possible. Where we have to edit for length, we ensure that the essence of the speeches, which are included, are properly reflected."
The Baftas, with or without political speeches, will screen Monday February 13 on UKTV.
This article originally appeared on the telegraph.co.uk