Staff at an exclusive private members’ club owned by a high-profile, Brexit-supporting backer of Boris Johnson are to go on strike.

Celebrities coming to 5 Hertford Street, which has hosted figures including George and Amal Clooney, Margot Robbie, Alexa Chung, Bella Hadid and royals such as Prince William, will have to consider whether they want to cross a picket line at the Mayfair property.

The industrial action is being taken by kitchen porters, all of whom are migrant workers demanding that they be paid the London living wage of £10.55 an hour and occupational sick pay that meets their needs.

The club, which is owned by the businessman Robin Birley, has been dubbed “Brexit HQ” by Brexiters. The activist Andy Wigmore tweeted a picture of himself at the club with Nigel Farage and the co-founders of the Leave.EU campaign group, Richard Tice and Arron Banks, on the anniversary in June of the 2016 referendum result.

An appeal to raise money for the workers’ strike fund was launched on Tuesday by the Independent Workers Union of Great Britain (IWGB), which counts 10 kitchen porters at the club as members. Nine of them have voted to go on strike, which will take place after talks this week, and the union is confident other workers will join them.

The IWGB’s president, Henry Chango Lopez, said: “By voting overwhelmingly in favour of strike action, the kitchen porters have sent a clear message that they will no longer be treated like the dirty dishes they clean.

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“The club can more than afford to pay these workers the London living wage and proper sick pay. If Robin Birley refuses these completely reasonable demands, he will be forced to serve his meals on dirty dishes because those that clean them are out on strike.”

A spokesperson for 5 Hertford Street said: “We are bemused by the IWGB’s attempt to persuade the tiny proportion of 5 Hertford Street staff it represents to go on strike.

“We already pay our kitchen porters £9.50 an hour – well above the minimum wage – and that pay rate will increase to the voluntary London living wage of £10.55 at the start of 2020. When their pay reaches that level, we will be one of a tiny proportion of London restaurants paying their kitchen porters the LLW.”

He added that the company also offered a range of staff benefits which go well beyond legal requirements, including private medical insurance and 25 days of holiday, plus bank holidays and an additional day off for birthdays.

“On the basis of this package, which is so well above the industry norm, we can only imagine that the IWGB has selected 5 Hertford Street for attention for PR and political purposes.”

The club was previously the target of protests and a campaign was launched earlier this year to support outsourced kitchen porters who say they were suspended after campaigning for the London living wage. The IWGB says that the club reversed the outsourcing decision following pressure.

Described by Vogue as “the loveliest club in London”, 5 Hertford Street was opened in 2012 by Birley, a property developer and long-time Brexit supporter, who previously donated to Ukip under Farage and gave at least £20,000 to Johnson before his victory in the Tory leadership race.