Why do London nightclubs close at 3am?

Didn't the UK Government allow 24 hour licenses? A bouncer told me that the London nightclubs made applications but they were refused. So why doesn't Westminister council want London to be a true late-night city. I see people who still want to go in clubs at 2am, but they're not allowed. I bet in New York, Los Angeles and Tokyo they're 24 hours.