Mew's orthotropics are considered fringe or pseudoscience because they lack the standard scientific support such as randomized controlled trials.
Sir, I was bemused to find myself reading the book review of J. Mew's book in the 9 May edition of the BDJ (216: 493) whilst the radio news announced another controversy regarding the publication of controversial research on statins in the BMJ. During my 25-year career as an orthodontist I have lost count of the number of times Dr Mew has had his controversial views published in the BDJ. Now he has self-published a 354 page book which costs £140, and is of 'limited relevance to the general practitioner or dental student, but specialists will be able to reach their own conclusions...' There is no information about from where this book can be obtained so it will not be easy for me indeed to do so. Is this really worthy of half a page of copy in our scientific journal? If there were a prospective controlled clinical trial to show the superiority of the techniques he has been promoting for so many years I would of course use them for the benefit of my patients, for that would be my professional duty.
[...] Perhaps it will come from the London School of Facial Orthotropics (of which J. Mew is a Professor) whose 'premises consist of one clinical room and one private consultation room'.
By the way, there are two Mews who promote orthotropics (J. and M.)
To be fair there are a some peer-reviewed papers by J. Mew, including one on tongue posture, but these seem to have low citation counts (~13). That 1981 paper in particular contains much of the same cases that are showcased in the OP's video.
There's a shorter (but freely available) 2005 article by J. Mew in which he complains that the field has been ignoring these tongue posture issues.
There's also an article in Vice titled "Mewing Is the Fringe Orthodontic Technique Taking Over YouTube". Among other stuff it says:
To understand how we got to a place where YouTubers are giving orthodontic advice, it's best to start with Dr. Mew himself, who you could call the original "mewing" YouTuber. His channel, Orthotropics, has been up since 2012 and hosts hundreds of videos about it.
"I'm here putting forward a very controversial point," he tells me, "saying that few people in the modern world have gained the full genetic potential in their facial development."
You'd assume Dr. Mew had coined the term "mewing," but that isn't the case. "I have no idea where it came from," he says. "I just started noticing it in the comments below the videos." [...]
Dig into Dr. Mew's channel and you'll find videos where he discusses being expelled from the British Orthodontic Society for his "social media postings," as well as a hearing with the General Dental Council in December last year. Dr. Mew wouldn't discuss any of this, citing legal reasons. When asked for comment, a spokesperson for the British Orthodontic Society said: "As we are not a regulatory body, we cannot comment on [an] individual's membership of BOS or status."
To check the orthodontic trade's feelings on the technique, I speak to Dr. Uchenna Okoye, who says she doesn't believe mewing is damaging; she has more issues with YouTubers who claim they whiten their teeth with bicarb and lemon. She adds: "I wouldn't disagree that there is benefit in some cases, but I wouldn't say it's the be all and end all."
That's as deep as this article goes in terms of scientific discussion.