Muslim leaders have condemned Nigel Farage’s call to ban public prayer by Muslims in the UK as bigoted and warned of a “growing tide of hate” after the Conservative leader, Kemi Badenoch, questioned whether the events fitted “within the norms of British culture”.

Farage was speaking at the launch of Reform UK’s manifesto for the forthcoming Scottish parliament elections when he made the remarks.

He described as “a wake up call and a warning to everybody” an event in Trafalgar Square earlier this week where hundreds of Muslims and people of other faiths prayed together, before the celebration of Eid.

He said the event, organised by the Ramadan Tent Project and attended by Sadiq Khan, London’s mayor, was “an open, deliberate, wilful attempt, not at the private observance of a different religion, but the attempt to overtake, intimidate and dominate our way of life”.

The event has happened in the historic square in central London five times before without incident or previous controversy.

Asked by a reporter if he would like to see such events banned in future, he replied: “We wouldn’t want to stop individuals praying but mass prayer is banned in many Muslim countries in the Middle East itself. So, yes, we have to stop this kind of mass demonstration, provocative demonstration, in historic British sites.”

Such restrictions vary from country to country, and could be related to political or religious tensions or public safety.

The former first minister and SNP MSP Humza Yousaf said: “Nigel Farage seems to have no issues with Christian prayer, Hannukah, Vaisakhi or Diwali all being celebrated in Trafalgar Square. He only has a problem with Muslims praying. There is a word for that, bigotry.”

Yousaf, the UK’s first Muslim first minister, added: “While I have come to expect nothing less from a charlatan like Nigel Farage, I am angry and disappointed that such rhetoric has been mainstreamed from the likes of Nick Timothy MP, a member of His Majesty’s opposition.”

Badenoch backed Timothy, her shadow justice secretary, after he claimed that Islamic prayers taking place in public were intimidating and unBritish, with Labour saying the Conservatives had embraced the “gutter” politics of prejudice.

Asked if she agreed with Timothy, or with arguments from other Tories that the main worry about the event was about prayers being separated for women and men, Badenoch said: “This debate which Nick is having is not about freedom of religion. It is about how religion is expressed in a shared public space, and whether those expressions fit within the norms of a British culture.”

The Scottish Labour leader, Anas Sarwar, said Farage’s remarks exemplified his “toxic, poisonous politics”. “The Farage circus came to town, and once again, he demonstrated that he is a cynical chancer who wants to divide us. Reform are just failed Tories and offer Scotland nothing.”

Recent opinion polls have put Reform neck and neck or ahead of Scottish Labour, but a Ipsos Scottish Political Pulse survey on Thursday suggested their popularity was slipping.

Shaista Gohir, a crossbench peer and leader of the Muslim Women’s Network UK, said: “When these gatherings are conducted responsibly – without obstructing roads, causing disruption, and with proper safety measures – why then do some politicians seek to ban them?”

“The answer is simple: they object to the sight of them. This reflects a deep-seated hatred toward Muslims. No other faith communities face comparable scrutiny or antagonism from these politicians in the way Muslims do”.

Akeela Ahmed, the chief executive of the British Muslim Trust, warned that British Muslims “must not become a political football”.

“Words have consequences – and those who genuinely believe in the British values of tolerance, equality under the law and freedom of religion must not allow those values to be cast aside in attempt to marginalise British muslims”.

Farage was speaking to a rowdy audience of about 500 supporters at a country club near Glasgow alongside his party’s Scotland leader, Malcolm Offord, as they introduced candidates for the Holyrood elections in May, where Reform UK will stand candidates in all seats.

Launching a manifesto that pledged Reform UK will “make Scotland the most successful part of the UK”, Offord said Scots were “being forced to pay the highest taxes anywhere in the UK” and repeated the promise to scrap Scotland’s six-band income tax system – in which higher earners pay significantly more.

Offord said that concerns about social cohesion in Glasgow, the UK’s biggest asylum dispersal area after London, were “not something we are making up”, and the manifesto pledged to restrict who can apply for homelessness support in the city.

The manifesto also pledged to scrap all the SNP government’s net zero related targets, subsidies and quangos.