Four-month-old Francis, from Walton in Liverpool, has acute myeloid leukaemia, which prevents bone marrow from making healthy blood cells.

The condition is most common in those over 75 and affects about 3,100 people in the UK each year - but doctors found Francis' bone marrow was 80% cancer cells in a biopsy over the summer.

While he continues to undergo chemotherapy, doctors have told the family his only chance of a cure would be a stem cell transplant.

It spurred mother Anna to encourage people aged 16 to 30 to sign the Anthony Nolan register, which connects patients with willing donors, in an attempt to find her baby a match.

That has now proved a success and his family has described match as a "huge weight" lifted from their shoulders.

"To find out Francis was in remission is a feeling we could never begin to describe. We were so sure that he wouldn't be, so to find out he was, was amazing," Anna added.

"We found out while Francis was smiling away and it was just a real pinch me moment."

Francis has just finished his second round of chemotherapy, which has been a "lot more intense" than the first, Anna said.

The family is now waiting for Francis' blood count to drop and rebuild, which leaves him vulnerable to illness in the meantime as his body can't fight infections.

But despite the gruelling treatment, Francis is "fine in himself at the moment".

"We can see where the chemotherapy is starting to take effect - but he is still smiling away," Anna said.

"He's gone into this round healthy so hopefully he manages the side effects better than last time."

When their world was 'turned upside down'

Francis' first tests took place when he was just six weeks old, and Anna had noticed a bruise on his arm that had no obvious explanation.

Further tests didn't suggest anything abnormal, but the diagnosis became clear when he was eventually given a bone marrow biopsy.

The news "completely turned our world upside down", Anna said - adding: "We would like to say a massive thank you to everyone who has signed up to the Anthony Nolan register.

"If people didn't sign up to the register, Francis wouldn't find a match.

"There are so many people in need and by someone taking a few minutes out of their day and signing up could save someone's life."

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Anthony Nolan's chief executive, Henny Braund, said "a number of perfect stem cell matches have been found".

"His journey is far from over, and we're continuing to support his family during this challenging time," he added.

"We extend our heartfelt thanks to everyone who has supported this appeal so far. We still need more people to sign up to the register who can offer a second chance at life to someone like Francis.

"Anyone can sign up to be a lifesaver by visiting Anthony Nolan's website and completing a short form, after which we'll send cheek swabs to them in the post for them to return to us."