The new policy was described as “nonsensical” and “completely unenforceable”.

“I have been out three times already,” said one employee. “People are still going out and having a fag. Everybody seems to be just ignoring the ban.”

Union representative Robin Hunter witnessed the demonstration and confirmed the numbers involved, pointing out it was not organised by the trade unions.

The demonstration was “a pretty obvious indication of how strongly people feel” about the ban, he said.

The health branch of the public service union UNISON is seeking legal advice regarding the new extended ban.

“We have now reached a turning point on smoking policy,” Mr Hunter said. “Up until now the unions have always supported the health board policy which, essentially, is about the prevention of harm through secondary smoking.

“We have supported the implementation of the statutory ban on smoking in enclosed public places. The new policy seems to us to cross the boundary into the area of human rights.

“There are all kinds of good reasons for restricting smoking, but we can see no good reason for an employer banning people from smoking in circumstances where there is no health risk to anyone other than the smoker.

“It is nonsensical to have a policy you will be totally unable to enforce. I think there is a strong chance the health board will bring itself in to disrepute through having a policy which it must know it cannot possibly enforce.”

Earlier, NHS Tayside conceded it would be relying on co-operation from staff and public to make the extended ban work, admitting it had no “smoke police” to enforce the new rules.

Earlier this year, NHS Tayside decided to exceed the requirements of national legislation prohibiting smoking in public buildings.

The authority said there was an onus on it to set an example.

Under the new rules, only in-patients are allowed to smoke on NHS Tayside grounds, and then only in designated shelters in hospital grounds.

Ninewells site manager Brian Main said today staff who persistently flouted the policy could face disciplinary action.

“This is going to be difficult,” he said. “I don’t think it is all going to be perfect from day one.

“It is a board policy. It is enforceable in terms of staff. Any member of staff who continues to flout the requirements can be dealt with if necessary. We are hopeful the public will support this, but all we can do is say to them ‘Could you please put out your cigarette?’

“I think there is enough of the general public who will appreciate what we are trying to do and, coming in to the hospital, they will not smoke. But it is very much a wait and see situation.”