There is nothing preventing the directors from forming a new business.  However, if the new company has the same or a similar name, or trading name, as that of the liquidated company, the directors can be held personally liable for the debts of the new company, unless they obtain the leave of the court.   They can also face a substantial fine or even imprisonment.  These are known as the 'phoenix company' provisions.

The main exception is where the new company buys the old company's assets from its receiver or liquidator.  In this situation the directors must write to all creditors of the old company advising them of the new company's formation.

Also, where directors are consistently involved with failed companies, they can be barred from acting as directors in future, on application to the Ministry of Business, Innovation and Employment or the Court.