If it's a limited company, Section 168 of the Companies Act 2006 applies. A director can be removed at any time by a properly convened meeting of the company's shareholders (who, in the case of a small company, might just be the directors anyway) where due notice of the resolution to remove the director has been given:
http://tinyurl.com/329v9cc
Individual companies might have additional procedures for removing a director written into their articles of association but such procedures would only apply to the relevant companies, not to all companies.
Chris