Like all other organisations, schools are entitled to have a no-smoking policy.
Unless there is an express term in an employee's contract allowing staff to smoke at work, they will have to comply with the school policy even if they were appointed before the no-smoking policy was implemented. The important principle is that the policy must be introduced for a legitimate purpose, which is likely to be the school's duty to safeguard the health and safety of staff, pupils and visitors.
There is no implied term in a contract of employment giving employees the right to smoke at work. The fact that such a policy might be hard on a particular member of staff does not justify the inference that a school has acted in such a way as to repudiate a contract with an employee.
Some schools provide a separate smoking room for staff, but there must be adequate ventilation, or other staff may claim that they have been injured by passive smoking.
It is not difficult to make a no-smoking policy. The governing body simply has to state that from a given date a no-smoking policy will be operated.
The main difficulty lies in introducing such a policy because of sensitivities on all sides of the argument about smoking at work.