Most people faced with such odds may have given up, but Brandon's fiancée, Kate Robertson launched a desperate bid to find a matching donor for her husband-to-be.
The odds paid off: less than a month after Miss Robertson's campaign was launched, a donor has been found.
Anthony Nolan said that her efforts has led to a 650% increase in people joining the bone marrow register. The blood cancer charity said that there was a particular surge among potential donors in the couple's home city of Bristol.
Miss Robertson, 31, said the response has been "astounding".
"It's been an incredibly difficult time so the relief we're feeling is overwhelming," she said.
"A matching donor means that we can go ahead with Mike's bone marrow transplant. We know we have a rocky road ahead as a transplant is a serious procedure, but knowing there is a good match for Mike is a fantastic boost that we desperately needed.
"We are hugely grateful to the selfless person who has stepped forward to help Mike, and to everyone who has pledged to do the same for someone else, by joining the Anthony Nolan register."
Mr Brandon, 29, was diagnosed with leukaemia in March.
The Oxford Brookes conservation and ecology graduate proposed three weeks before Miss Robertson headed off on a six-month backpacking trip at the start of the year.
But after her departure, he started suffering from fatigue and night sweats. He visited the doctor who carried out blood tests and within hours he learnt he had acute lymphoblastic leukaemia.
Miss Robertson, a physiotherapist, found out about her husband-to-be's condition while she was travelling in Burma. She immediately flew home to be at his side.
Mr Brandon's three brothers were tested as potential donors and were not correct matches.
So in May she launched her #Shake4Mike campaign - encouraging people to post pictures of themselves on social media shaking their heads to show that they had joined the bone marrow register.
Anthony Nolan said that more than 7,000 people applied to the register online between May 4 and 12, compared to 939 people during the same period in 2013.
"The response has been absolutely astounding," said Miss Robertson.
"Knowing that there is so much support out there and to be able to visibly see the results of what we are trying to achieve has lifted everyone's spirits. Both Mike and I have loved reading through the posts and messages that have been coming through. Some of the shaky faces really made us laugh out loud which was wonderful.
"The campaign was never just about finding a donor for Mike. Even at the outset we wanted to help make sure that there will be matching donors for other people going through the same agonising wait - other people's brothers and sisters, sons and daughters, mums and dads, and lifelong partners.
"We have been very lucky in finding a match but I know that not everyone is as fortunate. We still hope everyone will keep shaking their faces at cancer and continue to spread the #Shake4Mike campaign to help others in Mike's situation."
Ann O'Leary, head of register development at Anthony Nolan, added: "We are absolutely delighted that a matching donor has been found for Mike. His story inspired thousands of people to sign up as donors, any one of whom could go on to save the life of someone like Mike in years to come.
"It's our goal to find a match for everyone who needs a transplant so it's wonderful that Mike's friends and family are carrying on the fight against blood cancer and urging even more people to come forward and support the work of Anthony Nolan."
People aged 16 to 30 who are in good health can join the register online at www.anthonynolan.org.