Is the profession regulated?

Yes. In 1958 the Society of Teachers of the Alexander Technique (STAT) was started in the UK,

FM walking in the field It was the first professional Alexander Technique society in the world. The Dutch Society of Alexander teachers (NeVLAT) was founded in 1996. On the website of the Alexander Technique Affiliated Societies (ATAS) you can find the names and addresses of affiliated societies. ATAS consists of 15 national societies of teachers which maintain the highest standards for the training and professional conduct of Alexander Technique teachers.