Where the premises concerned holds a licence under the Licensing Act 2003 for Regulated entertainment (and you have permission of the licence holder to perform) then no authorisation under the Hypnotism Act is required unless there are conditions on the licence that require a separate Hypnotism authorisation to be obtained. The premises licence may already impose conditions in respect of Hypnotism (in which case these must be complied with).
Where the premises concerned does not hold a licence for Regulated entertainment under the Licensing Act 2003 then an authorisation under the Hypnotism Act (by way of application) is required.
Hypnotism includes mesmerism and any similar act or process which produces or is intended to produce in any person any form of induced sleep or trance in which the susceptibility of the mind of that person to suggestion or direction is increased or intended to be increased. It does not include hypnotism, mesmerism or any such similar act or process which is self-induced. In addition, exhibitions, demonstrations or performances of hypnotism that take place in the course of a performance of a play are exempt from any licence or authorisation requirement.