The Union Jack-related comments by the UK's Labour councillors and candidates are "despicable", the Daily Mail has cited an unnamed insider as saying.
The source added that many Labour voters in the city of Warrington in Cheshire will be "appalled" to know that "prospective candidates and councillors have been talking about the union flag and national anthem in such a derogatory, un-British manner".
Their leaked comments were earlier posted as part of a debate about the flying of the Union Jack in the Labour Party's WhatsApp group.
The discussion kicked off after former MP-turned-Labour candidate Faisal Rashid asked fellow party members whether Union flags "should fly every day" and "Are flags a sign of unity and patriotism or do they divide us?"
Election candidate Amy Brooks responded by arguing that she "personally" does not "agree with it, [because] many use the flag to push non-inclusive agendas".
Robin Frith, another election candidate and secretary of Warrington North Constituency Labour Party, in turn, asserted that flying the Union Jack was "another move from the Fascist playbook".
The debate reportedly continued with Councillor Paul Warburton claiming the "next step" will be "teaching the national anthem in schools and the singing of it each morning at the raising of the flag".
Warburton's remarks were ostensibly then commented on in the same tone by another politician, Rebecca Knowles, who serves as cabinet member for adult social care.
"It's chilling. There's nothing at all wrong about being proud of your nationality but this all feels pretty creepy and I must say as the mum of a biracial family it makes me feel very nervous indeed", Knowles argued.
In early February, The Guardian reported about a leaked memo which said that Labour should "make use of the flag, veterans, and dressing smartly" as part of the party's radical rebranding.
An array of left-wing MPs, including former shadow cabinet ministers Clive Lewis and Richard Burgeon, criticised the new strategy, claiming that it risked alienating young as well as Black, Asian, and ethnic minority voters.
