Under the Companies Act 2006 a private company no longer needs to have a company secretary (section 270) however a public company does need one (section 271).
In practice most private companies will continue to have a company secretary. The company secretary is in charge of the administrative side of running the company, exactly what the company secretary does will depend upon the company itself. Many solicitors and accountants also offer company secretarial services.
Usually the company secretary will be required to write up the minutes of board and general meetings, deal with returns and other documents for the Registrar of Companies and keep the companies internal registers up to date.
The only specific requirement for a company secretary is in relation to public companies. To be a secretary of a public company the Companies Act 2006 (section 273) specifies that you must be specifically qualified. Examples of those that are specifically qualified include solicitors, accountants and chartered secretaries.