A professional recording studio will typically have a live room where instrumentals and vocals take place, and a control room, where the sound engineer will control the audio for analogue or digital recording in order to create and record the best possible sound.
An isolation booth is also quite common. It can be used to record vocals to get a crystal clear sound, or to record louder instruments, such as drums, without the sound being picked up by other microphones recording vocals or quieter instruments. It can even be used for an acoustic instrument where the sound needs to be perfect. Some studios may have instruments available to use, but sometimes you will probably have to bring your own.
Rehearsal spaces may also be available, whether in the same room as the recording studio or a separate space within the same building. Rehearsals for dance routines will obviously need a bigger space, such as a hall or professional dance studio with minimal expensive equipment around, as it could get broken if knocked.
When hiring a studio, it will usually come with a producer, who perhaps owns it, or one who you have chosen to work with. If you or someone within your party has experience with sound engineering then you may not need a producer when you hire a studio.
London studios are usually a lot more expensive than other locations around the country, as the demand is higher here, with the majority of the entertainment industry living in the capital. Looking online at various different studios will bring up some more information for you and also help you to compare prices and features in order to find the best possible option for your needs.