loosely speaking the conservatoire audition process is broken in to 3 stages open days, Applications and Auditions
Open days for conservatoire begin in January and run as late as september. When you arrive there is generally a talk for all perspective students where the head of the conservatoire will basically tell you all the reasons to go there. they will also often outline the day and briefly mention Accomodation and finances although there are often separate talks on theese as well as tours of the accomodation. Obviously as theese are performance schools every talk you sit on whether its a generall talk or a more specific department talk there will be someone playing something. When I went to birmingham there was even people playing at lunch time.
Between open days and applications there is another sort of mini step. Many coservatoires offer the option to pay for a consultation lesson with the current teacher of your instrument there. Although theese are expensive they can actually help you out at the audition step because you can bet your bottom dollar they will show up again in your audition as they are obviously the most qualified person to make a decision on whether you are good enough.
The next step would be to sybmit your application form. the deadline for conservatoire applications is often the 1st of october although you can check the deadline for your year on UCAS. The application process isn't all together that different from other applications however obviously when you write your personal statement ect you want to emphasise your performance history ect. It would be a really good idea to look for local competitions before you get to this step because winning a category there would really give your application a boost.
The final step is the audition. Auditions for conservatoire places aren't guaranteed however they are likely as since you have to pay they are a great way for the conservatoire to make money. depending on which conservatoire your auditioning for you may get to choose your own pieces or you may have to play one of their set pieces. make sure you check this early because if you leave it too late you may not have time to learn your pieces well enough. usually the conservatoire will provide an acompanist however in some cases you may be able to bring your own. either way its a good idea to practice with an acompanist before hand as on the day you wont get time for full run throughs just top and tailling. You may also have other parts to your audition like sight reading, scales, improvisation, scales, singing, transposition or theory tests. you can usually find out on their website.
finally you have to wait for the results which usually come in towoards the end of december.
Good luck!!