James Cleverly has said he disagrees with his Conservative frontbench colleague Nick Timothy’s assertion that public Muslim prayers are an act of domination, as another senior Tory called for the party to respect the right to worship.

Kemi Badenoch has defended Timothy, the shadow justice secretary, after he posted images of mass prayer at a Ramadan event on Monday evening in Trafalgar Square, calling it “an act of domination” and “straight from the Islamist playbook”.

His remarks sparked significant condemnation, with Keir Starmer calling for Badenoch to sack Timothy; while Richard Hermer, the attorney general, has challenged the Conservative leader to say whether she would object to Jewish prayer in public.

In the most open criticism of Timothy by a senior Tory so far, Emma Best, the party’s deputy leader on the London assembly, said prayer was “a fundamental right of every UK citizen” and that if people did not like this, it was their problem.

Speaking on BBC One’s Sunday with Laura Kuenssberg, Cleverly, the shadow communities secretary, said Timothy had been correct to begin a debate about Monday’s “Open Iftar”, the last of 18 such public events at which anyone can join the breaking of the Ramadan fast at dusk.

But asked if he concurred with Timothy’s argument about the large-scale Muslim prayer in public being an act of domination, Cleverly said: “So, that wouldn’t be my personal take.”

Badenoch and some other Conservatives have largely framed their objection to the Open Iftar on the basis of gender segregation. Cleverly continued on this theme, but appeared to suggest that the whole event was separated, when it was not – men and women prayed separately, but otherwise mixed freely.

Asked why the Conservatives objected to a Muslim event on Trafalgar Square, but had no concerns about earlier Christian, Sikh and Jewish events in the same place, Timothy argued that the difference was that women were not “segregated” at any of these.

Cleverly said: “What the point Nick was making is that this type of ceremony in the public space, where women were segregated from men, is at odds with a lot of the norms and traditions of the UK.”

But speaking on the BBC’s London Politics show, Best disputed this characterisation, saying some fellow London Conservatives had attended Monday’s event without concern, and that the prayer was only a small part of it.

“When it comes to this iftar event, there were thousands and thousands and thousands of people there,” she said.

“I had friends and colleagues that went. Many people chose not to pray. In fact, the large majority of people celebrating chose not to pray, and that wasn’t what the event was about.

“So I agree with the organisers. There’s been a slight misrepresentation here.”

Best said she did not want her party to be talking about bans on public prayer.

She said: “I don’t want to live in a secular society. I want to live in a society where everybody in my family, my friends, my children, are free to practise whatever religion they want.

“Do I agree with Nick Timothy on this? No, I think prayer is a fundamental right of every UK citizen, and if you don’t like it, walk on.”