The smoking ban in England is the "single most important public health legislation for a generation", Health Secretary Alan Johnson has said.
Sign of the times: Pub smokers have to stay outside
He said the ban on smoking in enclosed public places, which came into force on Sunday, would improve the health of hundreds of thousands of people.
But there have been isolated signs of opposition to the smoking clampdown.
The landlord of a bar in Herefordshire and the boss of a London lapdancing club have vowed to challenge the ban.
Pubs, clubs and restaurants - and all enclosed public places - are now smoke-free zones, a change which Mr Johnson said was popular with 80% of the population.
The chief medical officer for England, Sir Liam Donaldson, told the BBC that he expected the regulations to be implemented without any substantial problems.
"The majority of smokers and non-smokers wanted this change, so I expect people to comply with it very, very straightforwardly," he said.
But Dave West, owner of a central London lapdancing club, said he would allow staff and customers to continue to smoke - claiming that the ban is a breach of human rights.
Club owner Dave West plans to challenge the smoking ban
And Tony Blows, landlord of the Dog Inn at Ewyas Harold, Herefordshire, threatened to allow customers to carry on smoking.
Owners and managers of pubs and clubs which fail to comply with the smoking laws can face fines of up to £2,500 - and individual smokers can be fined £50.
There have been divided forecasts over the impact of the smoking ban on pubs.
The Campaign for Real Ale (CAMRA) says its surveys suggest that very few people will be deterred from going to pubs - and that 840,000 people who currently do not go to pubs would become more likely to go to smoke-free pubs.
However the British Beer and Pub Association anticipated that beer sales would drop.
Trade union leaders have applauded the curbs on smoking in England as a step forward for workplace safety - describing passive smoking as the "third biggest cause of deaths at work".
But smokers' rights group, Forest, attacked the ban saying that it is "out of all proportion to the risk from second-hand smoke".
Scotland, Wales and Northern Ireland already have similar bans in place.