Yes, the criminal courts have power to disqualify directors, and breaching an order carries criminal sanctions. No, in practice most disqualifications are made in the civil courts. There is a separate civil procedure to disqualify directors who have been inept or negligent but not criminal. This takes place in the Companies Court. The Companies Court is part of the Chancery Division of the High Court.
Businesses fail for all sorts of reasons.
The businessman has lost his livelihood. He has probably staked everything he owns in the venture. Orders under the Company Directors Disqualification Act 1986 disqualifying a businessman from acting as a director can have a crippling impact on him and his family. The order not merely disqualifies him from being a director but from being involved in the management of a company at all. For a person who has spent his life self employed and running his own business the impact of a disqualification can be colossal.