There are two separate issues here:
Firstly, any pub is free to make their own rules (as long as they don't conflict with the law) about who they will, or won't admit. One pub I go into has a strict 'Over-18s only' rule. There are a small number of pubs that insist on 'Over-21s only'' and even a few that are 'Over-25s only'. Hc4361's link explains J D Wetherspoon's policy.
However pubs (and pub companies) can't change the law. The Licensing Act 2003 makes it an offence for a licensee (or anyone else who is empowered to request a child to leave, such as member of the bar staff) to permit a person under 16 years of age to be on licensed premises unless they're accompanied by a person over the age of 18:
http://www.legislation.gov.uk/ukpga/2003/17/section/145