The pay of directors of public companies is no business of government. It is very much the business of the owners of those companies - you and I, anyone with a pension pot. Currently directors' pay is determined by a remuneration committee, whose members are appointed by, er, the directors.
It is a simple matter to change membership of the remuneration committees to persons appointed by the shareholders, or in the case of institutional investors (often themselves also plcs) their own investors. This will result in bonus structures where bonuses are paid where the return to shareholders is good, and withheld when it is not. It will go far to end the culture of obscene and unwarranted levels of pay amongst those at the top of public companies.