The 30-year-old from North Kilworth, Leicestershire collapsed in Birdcage Walk near Buckingham Palace, less than a mile from the London Marathon finish line.
Friends say Claire was running for the Samaritans in memory of her brother, who died at 25. Grant Squires died from an overdose in 2001 after becoming depressed following a car accident in which he survived, but his girlfriend Heidi Richardson was killed.
She also chose the charity to honour her mother, who has volunteered for the Samaritans for years.
“Claire chose to run the marathon for Samaritans as her mother Cilla Squires has been a volunteer for the charity for 24 years,” Catherine Johnstone, chief executive of Samaritans, said.
“We desperately wish that it was not under these circumstances but we have been overwhelmed by the response from people donating in Claire’s memory.
“These donations will be put into a tribute fund and, following discussions with the family, will go towards projects they feel would have been important to Claire.”
Claire completed the London Marathon in 2010 and last year climbed Mt Kilimanjaro in Tanzania to raise money for the Royal Air Force Association.
She is the tenth runner to die during the race since the London Marathon began in 1981. Tests to discover why she collapsed are expected in the coming days.
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