Can my employer stop smokers from taking cigarette breaks?

Workers are entitled to breaks and what they do in these breaks is a matter for them, so long as it is not on the employer's premises. Therefore it would be very difficult for an employer to insist that a worker does not smoke in their lunch break or coffee break.

They can however insist that smokers do not take additional breaks, but most employers will try to take a relaxed attitude and accept that if people want to smoke, imposing restrictions is not going to help morale and some breaks, within reason, are acceptable. Your employer should have a clear policy on smoking breaks, and any breaches of the policy should be dealt with fairly and consistently. If it becomes a disciplinary issue, your employer should follow its disciplinary policy.