The prime minister urged people to take part in a "spit drive" this weekend to find a stem cell match that would lead to a life-saving transplant for Lara Casalotti, 24, a mixed-race woman suffering from blood cancer.
Lara, from Hampstead, was diagnosed with leukaemia just before Christmas and needs a stem cell transplant by April to save her life.
However, her Thai-Italian heritage makes it extremely difficult to find a donor: only three per cent of the worldwide donor register are mixed race, and an even tinier fraction are a similar ethnic mix to her.
After finding out that her only brother Seb was not a match, Lara's family launched a campaign aimed at finding her a donor, as well as encouraging more mixed-race people to sign up to diversify the register.
"We're trying to find a needle in a haystack and need all the help we can get," said Lara's mother, Supanya, 53.
Thousands of people attended a #Match4Lara spit drive at the 02 centre in north London on Saturday.
The hunt for a suitable donor for Lara has sparked one of the biggest ever global campaigns of its kind, the Anthony Nolan cancer charity said in a statement.
Since launching the Match4Lara campaign just over two weeks ago, the charity said it had recorded an “unprecedented” spike in registrations, with over 7,000 new online applications and even more joining up at donor drive events.
If you'd like to help, upcoming spit drives in London are:
29th January, Hounslow Jamia Mosque, 12-2pm
31st January, Jewish Museum, 10am-3pm
31st January, Parish Centre, Thirleby Road, Edgware 9am-3pm
Learn more about the campaign and how donation works at Match4Lara.