Members of the public should challenge casual racism, standing up to those who verbally or physically abuse others on the basis of their faith or ethnicity, Jeremy Corbyn has said.

Speaking at a service at Finsbury Park mosque to mark two weeks since the north London terror attack in which one person died and several others were injured, the Labour leader said all forms of racism and discrimination should be challenged at all times.

He drew attention to “what is unfortunately called ‘casual racism’, when Muslim women on buses, when Muslim women on trains are abused and no one challenges it”.

Corbyn said: “They’re isolated, they’re alone, they’re frightened – and the result will be they’re probably afraid to go out in the future. It is a question of not just declaring today our strength of community and unity, [but] our ability to do that every day, all the time, if we want to live in the decent non-racist society that we all crave.”

Police in Manchester and London registered surges in anti-Muslim hate crime in the immediate aftermaths of the Manchester Arena bombing and the London Bridge attack.

Two Muslim cousins in east London were attacked with acid on 21 June, two days after the Finsbury Park attack, in what police later designated as a hate crime. Jameel Muhktar and Resham Khan suffered severe burns and life-changing injuries.

Other examples include Naveed Yasin, a trauma and orthopaedic surgeon who helped save the lives of people injured in the Manchester attack, who was racially abused and called a terrorist on his way to work at Salford Royal hospital, and women having their head scarves ripped from their heads or being spat at.

The Met police said they had recorded 1,260 incidents of hate crime in the 12 months to March, compared with 343 incidents in the 12 months to March 2013.

Speaking at Monday’s service at Finsbury Park mosque, Fiona Taylor, a temporary assistant commissioner at the Met, said attacks this year in London and Manchester “highlight the resilience of a multicultural and multifaith society … and strengthen the resolve of the Metropolitan police service to tackle hate crime, which if left unchecked can lead to more violent extremism.

She added: “We recognise the damaging effect that [hate crime] has on victims and on communities, and we recognise that too often victims suffer in silence. We know that there is much more we can do, and we are committed to doing as much as we can to stamp out hate crime in this city.”

The congregation included uniformed members of the emergency services, local councillors and representatives of faith communities. Relatives of Makram Ali, the 51-year-old man who died when a van swerved into a crowd of people outside the nearby Muslim Welfare House, were also present.

Speaking on their behalf, Shah Islam said the family had lost a husband, father, brother and grandfather in a “heinous act of terrorism [which was] a clear manifestation of hate crime and Islamophobia”.

But, he added, “we hold no grudges against anyone, not even the misguided attacker … We should realise that we are at our best as humans when we build bridges, not walls.”

Many of the speakers highlighted the community’s united response to the attack, and the positive relationships between local mosques and other faith groups and non-faith organisations.