Directors can be removed from office:
(1) under CA 2006, sec168 by ordinary resolution;
(2) under provisions in the articles (see, for example, provisions in the Model Articles if registered from 1.10.2009, or Table A for earlier companies);
(3) if disqualified from acting.
CA 2006, sec168 (1) A company may by ordinary resolution at a meeting remove a director before the expiration of his period of office, notwithstanding anything in any agreement between it and him.
(2) Special notice is required of a resolution to remove a director under this section or to appoint somebody instead of a director so removed at the meeting at which he is removed.
(5) This section is not to be taken (a) as depriving a person removed under it of compensation or damages payable to him in respect of the termination of his appointment as director or of any appointment terminating with that as director, or (b) as derogating from any power to remove a director that may exist apart from this section.
The special notice provisions are set out in sec312 CA 2006. This provides that the resolution is not effective unless notice of the intention to move it has been given to the company a least 28 days before the meeting at which it is moved. The company must then give notice of the resolution at the same time and in the same manner as it gives notice of the meeting (or, if that is not practicable, must advertise in an appropriate newspaper).
The ability to remove a director by ordinary resolution cannot be excluded by the articles (see sec168(1) above). It can in practice be avoided by inserting in the articles a provision usually known as a "Bushell v Faith clause". Such a clause confers enhanced voting rights on the director who is being removed (provided he or she is also a shareholder). Typical wording is:
"Every director of the company has the following rights in the event of a poll being duly demanded at any general meeting:
(a) if the poll is so demanded on a resolution to remove that director from office, to  votes for each share held by her/him; and
(b) if the poll is so demanded on a resolution to delete or amend the provisions of this article, to  votes for each share held by her/him."
Note that this clause can only a protect a director who is also a shareholder in the company, and the above wording will have to be modified to meet the circumstances of each case.
Removal under the articles
Model Articles, Article 18 provide that a person ceases to be a director as soon as-
(a) that person ceases to be a director by virtue of any provision of the Companies Act 2006 or is prohibited from being a director by law;
(b) a bankruptcy order is made against that person;
(c) a composition is made with that person's creditors generally in satisfaction of that person's debts;
(d) a registered medical practitioner who is treating that person gives a written opinion to the company stating that that person has become physically or mentally incapable of acting as a director and may remain so for more than three months;
(e) by reason of that person's mental health, a court makes an order which wholly or partly prevents that person from personally exercising any powers or rights which that person would otherwise have;
(f) notification is received by the company from the director that the director is resigning from office, and such resignation has taken effect in accordance with its terms.
Table A, article 81 provides that the office of a director shall be vacated if -
(a) he ceases to be a director by virtue of any provision of the Act or he becomes prohibited by law from being a director; or
(b) he becomes bankrupt or makes any arrangement or composition with his creditors generally; or
(c) he is, or may be, suffering from mental disorder and either -
(i) he is admitted to hospital in pursuance of an application for admission or treatment under the Mental Health Act 1983 or, in Scotland, an application for admission under the Mental Health (Scotland) Act 1960, or
(ii) an order is made by a court having jurisdiction (whether in the United Kingdom or elsewhere) in matters concerning mental disorder for his detention or for the appointment of a receiver, curator bonis or other person to exercise powers with respect to his property or affairs; or
(d) he resigns his office by notice to the company; or
(e) he shall for more than six consecutive months have been absent without permission of the directors from meetings of the directors held during that period and the directors resolve that his office be vacated.
Other grounds could be added to the articles and/or provisions inserted to make it easier to remove a director.
A court may make a disqualification order prohibiting the person from acting as a director of a company, or being involved in the management of any company, for the period of the disqualification. Such orders are made under the Company Directors Disqualification Act 1986.
Note that if the director is removed from office as a director, this will not usually affect the director's position (if he/she has one) as a shareholder in the company. This is often a relevant consideration in private companies, where often a director is also a shareholder. In most circumstances the only solution is for there to be negotiations for the purchase of the ex-directors shares. In some circumstances, the removal of the director may be grounds for petition under CA 2006, sec994 (the unfairly prejudicial conduct provision) under which the court may order the remaining shareholders (or indeed, The Company itself) to buy the ex-directors shares. Some companies' articles contain a clause that a shareholder who ceases to be a director is deemed to have given the company a transfer notice in respect of his or her shares, so that the shares can, in effect, be compulsorily acquired.
Company Law Solutions can advise on the correct procedure for the removal of a director, and prepare the accompanying documentation.