In terms of specific regulated entertainments please note that:

plays: no licence is required for performances between 8am and 11pm on any day, provided that the audience does not exceed 500
films: no licence is required for ‘not-for-profit’ film exhibition held in community premises between 8am and 11pm on any day provided that the audience does not exceed 500 and the organiser (a) gets consent to the screening from a person who is responsible for the premises; and (b) ensures that each such screening abides by age classification ratings
indoor sporting events: no licence is required for performances between 8am and 11pm on any day, provided that the audience does not exceed 1000
dance: no licence is required for performances between 8am and 11pm on any day, provided that the audience does not exceed 500. However, a performance which amounts to adult entertainment remains licensable.
boxing or wrestling entertainment: no licence is required for a contest, exhibition or display of Greco-Roman wrestling, or freestyle wrestling between 8am and 11pm on any day, provided that the audience does not exceed 1000. Combined fighting sports – defined as a contest, exhibition or display which combines boxing or wrestling with one or more martial arts – are licensable as a boxing or wrestling entertainment rather than an indoor sporting event

Live music

No permission is required for:

a performance of unamplified live music between 8am and 11pm on any day, on any premises
a performance of amplified live music between 8am and 11pm on any day on premises authorised to sell alcohol for consumption on those premises, provided that the audience does not exceed 500
a performance of amplified live music between 8am and 11pm on any day, in a workplace that is not licensed to sell alcohol on those premises, provided that the audience does not exceed 500
a performance of amplified live music between 8am and 11pm on any day, in a church hall, village hall, community hall, or other similar community premises, that is not licensed by a premises licence to sell alcohol, provided that (a) the audience does not exceed 500, and (b) the organiser gets consent for the performance from a person who is responsible for the premises
a performance of amplified live music between 8am and 11pm on any day, at the non-residential premises of (i) a local authority, or (ii) a school, or (iii) a hospital, provided that (a) the audience does not exceed 500, and (b) the organiser gets consent for the performance on the relevant premises from: (i) the local authority concerned, or (ii) the school or (iii) the health care provider for the hospital

Recorded music

No permission is required for:

any playing of recorded music between 8am and 11pm on any day on premises authorised to sell alcohol for consumption on those premises, provided that the audience does not exceed 500
any playing of recorded music between 8am and 11pm on any day, in a church hall, village hall, community hall, or other similar community premises, that is not licensed by a premises licence to sell alcohol, provided that (a) the audience does not exceed 500, and (b) the organiser gets consent for the performance from a person who is responsible for the premises
any playing of recorded music between 8am and 11pm on any day, at the non-residential premises of (i) a local authority, or (ii) a school, or (iii) a hospital, provided that (a) the audience does not exceed 500, and (b) the organiser gets consent for the performance on the relevant premises from: (i) the local authority concerned, or (ii) the school proprietor or (iii) the health care provider for the hospital

No licence is required between 8am and 11pm on any day, with no limit on audience size for:

any entertainment taking place on the premises of the local authority where the entertainment is provided by or on behalf of the local authority
any entertainment taking place on the hospital premises of the health care provider where the entertainment is provided by or on behalf of the health care provider
any entertainment taking place on the premises of the school where the entertainment is provided by or on behalf of the school proprietor
any entertainment (excluding films and a boxing or wrestling entertainment) taking place at a travelling circus, provided that (a) it takes place within a moveable structure that accommodates the audience, and (b) that the travelling circus has not been located on the same site for more than 28 consecutive days