Donations on the 30-year-old's JustGiving page have risen to over £500,000, with her family urging people to keep on giving.
In a statement, the 30-year-old's family said :
Martha Fairlie reports on the legacy of Claire Squires:
The hairdresser from Leicestershire, collapsed in Birdcage Walk, near St James's Park, close to the end of the 26.2 mile course. Tests to establish why she died are expected to take place in the coming days.
Ms Squires has been called an "inspiration" by her close friend Nicola Short. The pair climbed Mount Kilimanjaro for the RAF Association last year, raising £1,500.
Ms Squires was running the marathon for the Samaritans because her mother has volunteered with the charity for more than 20 years.
She was also motivated to run for them due to the death of her brother from an overdose, the Daily Telegraph report.
Samaritans' Rachel Kirby-Rider told ITV News that they were "devastated" on hearing about her death, and expressed their condolences to her family.
Victoria Hauser, who had known Ms Squires for 15 years, called her "the most amazing person in the world", in an interview with 5 News.
Tributes have also poured in from people on the social media website Twitter.
The London Marathon organisers sent their "condolences" in a statement on their website.