Mike Haines, 51, who has campaigned for peace since his Yorkshire-born humanitarian worker brother David was beheaded by IS, told the largely Muslim crowd: “It is important that we react in a positive way against these hate-mongers. “
The event was organised by grassroots Muslim groups to mark the religious festival of Ashura.
It is a time which carries key messages about the importance of justice, freedom and the idea there should be no justification of wrongdoing in the name of religion.
Mr Haines spoke of how his younger brother was held captive for 18 months, beaten and tortured along with other hostages before being murdered on September 13 2014.
His family’s trauma was deepened when his death was filmed and posted on the internet.
Struggling to hold back tears at times, particularly because it was so close to the anniversary of his brother’s death, Mr Haines said: “I mourn my brother every day.
“However he knew the risks of being a humanitarian worker.
“He and my family accepted those risks because he was doing important work, helping his fellow man regardless of creed, colour, race or religion.”
The retired mental health nurse from Dundee condemned the “truly disgusting atrocities” carried out by IS and others against innocent people.
He said: “The callous murder of my brother, the bombing of a teenage concert in Manchester, the deplorable attack on a place of worship in Finsbury Park, the inexcusable name-calling of people based on their religion or colour - they all have one thing in common which is to incite hatred.”
He said hatred “steals the humanity from a person” and society must not allow this destruction to win.
Mr Haines added: “It is only by working together that we can combat the hatred of the extremists.
“It starts on a very basic level as individuals and then pervades upwards through the strata of our society.”
Thousands of Muslims turned out for the demonstration which started at Hyde Park and worked its way through central London.
People of all ages, including families and children, were among those who took part, with some holding banners which read “Muslims condemn terrorism” and “180K imams have spoken against IS”.
Some finished the demonstration with prayers at a mosque, while others headed to Trafalgar Square.