But he might still be on the waiting list, enduring 12 hours of dialysis each day, if his mother, Nicola, had not run a Facebook campaign to find him a living donor.
Matthew is one of a number of UK patients who have bypassed the traditional NHS system of organ allocation, instead harnessing the power of the internet to find their own.
Transplant doctors fear this development could result in an unsavoury competition to attract donors online, in what some have called an “organ beauty pageant”.
And they worry that it rips up the traditional health service ethos of equal access to treatment for all.
Consultant nephrologist Dr Adnan Sharif, from Birmingham’s Queen Elizabeth Hospital, says: “Somebody who is well-to-do, a professional, will be very good at promoting themselves,” whereas poorer patients, perhaps from minority ethnic communities, will not have the same opportunities.
But Matthew’s mother is unrepentant.
“I’m not going to lie, I think on Matthew’s side was the fact he was a child,” she says.
“In all walks of life, we use things to our advantage.
“If it meant that he didn’t have to spend his life on dialysis, then I’d take it – I don’t care.”
There are 28,000 people on dialysis in the UK.
Some 5,000 patients are on the national waiting list for an organ transplant from a dead donor.
There is a permanent shortage of such kidneys.
But there is another option; they may get a kidney from a living donor, because most of us can live healthily with just one.
Living donors now make up a third of all kidney transplants in the UK.
Some are donated anonymously through a very successful NHS scheme.
But social media campaigns such as Matthew’s can bring dozens of would-be donors to be tissue-tested for just one patient, squeezing resources.
Sue Moore, the lead NHS living donor coordinator in Birmingham, says: “You’d get people call out of the blue, and it was quite overwhelming really.”
However, since Matthew’s appeal was launched in 2013, Queen Elizabeth Hospital, the biggest renal centre in Europe, has adjusted to handling such pressures.
Matthew’s mother argues publicity for his campaign increased awareness of kidney donation.
And some of the people initially tested for Matthew went on to give a kidney to someone else.
One was Alison Thornhill, who was touched by his Facebook appeal.
“If one of my grandchildren was in that situation, I would want somebody to step forward and be tested to see if they were a match for him,” she says.
Alison wasn’t a match for Matthew, but since she “was prepared to give a kidney to a little boy who I didn’t know, it made sense just to go on and give it to somebody else who I didn’t know who needed it”.
Eighteen months ago, she went into hospital and became an anonymous donor.
Unexpectedly, she later got letters from the recipient, and from his mother, who wrote: “I don’t know anything about you apart from the fact that you are a very kind and compassionate person.
“I will be eternally grateful to you.
“Kindest regards, a loving and thankful mother.”
But some would-be donors want to choose precisely who receives their kidney.
Searching online, Gemma Coles identified a series of patients she wanted to donate to, though for various reasons it has not yet happened.
Asked why she wants to choose the recipient, she replies she has only one kidney to give.
“You have to be judgemental,” she says.
“There’s thousands of people, literally, needing a kidney, and more and more now their stories are available on social media, and it can feel you’re being very critical of people’s lives, trying to decide who to give and who not to.”
If the transplant community was disturbed by Facebook kidney appeals, it was shocked by websites offering to match donors and patients, who can browse through profiles and photos.
Matchingdonors.com was set up in the US by businessman Paul Dooley as a non-profit venture.
It charges $595 (£464) for US patients seeking a donor.
In 2012, he brought the website to the UK, but this time, without charging any fees.
According to the regulator, the Human Tissue Authority, transplant centres must refuse operations involving a website that does charge fees.
Since Matchingdonors.com is free to use in the UK, there is no regulatory barrier to stop it brokering a transplant.
But chief executive Mr Dooley says not one such transplant has taken place in five years in the UK.
There are 73 UK patients waiting – some have found matches with potential donors, but none has had permission from their hospital to go ahead.
In 2015, he stopped stopped signing up British patients, because “there’s no use them going to a gas station if there’s no gas”.
It seems the transplant community simply decided organ-matching websites were beyond the pale. But is this fair?
Prof Vassilios Papalois, who formerly chaired the British Transplantation Society’s ethics committee, says the views of transplant teams must be respected.
“They have the autonomy to say that for us it’s ethically objectionable,” he says.
Asked if he is trying to provide the catwalk for an organ beauty pageant, Mr Dooley replies: “Every single person on our website who’s an organ donor wants to choose.
“They want to say, ‘I want to give to an old grandfather, ‘I want to give to a single father,’ and if that’s what they consider a beauty contest, that’s not a beauty contest, it’s the choice of who you want to donate to.”