FDS is the Federation of Drama Schools:
https://www.federationofdramaschools.co.ukCDMT is The Council for Dance, Drama and Musical Theatre:
https://cdmt.org.ukConservatoires are signed up with these organisations which means they have achieved a certain level of quality when it comes to professional training in Acting and MT. When you click on the schools listed with then you will see some very well known and very well respected drama, dance and MT schools, from RADA and ArtsEd (FDS) to Mountview and English National Ballet School (CDMT).
There are some places out there that are not particularly scrupulous and happy to take people's money without providing the quality and rigour in their training that is required by industry. The industry is already insanely competitive so the last thing you want to do is spend 3 years training somewhere only to find that it is not respected in the industry and you cannot work. Do your homework and use the FDS and CDMT as the starting point for your research into the different drama schools. It will also allow you to see the what their alumni are doing and the application process (audition requirements: number of monologues, modern and Shakespeare etc.).
Also, I am sure that you have been told how difficult it is to get into drama school. For example: LAMDA has 30 places on its BA Professional Acting course but receives well over 3,500 applications for this course alone every year, that is less than a 1% acceptance rate. Whereas Urdang get 2,000 applicants for 150 places on the BA MT course, so their acceptance rate is 8%.
There is a really useful book that goes through all of this, I will see if I can find it. If I do, I will post it here.