Nearly all businesses are complying with the ban, say figures from the Department of Health (DoH).
The survey of local authorities found 97 per cent of businesses inspected in the two weeks after July 1 were smoke-free as required by the new law.
The South-West region had the lowest rate of compliance but even here 94 per cent of businesses were upholding the law.
Councils have so far issued 142 written warnings following failure to prevent smoking (equivalent to 0.2 per cent of premises inspected), and issued only one fixed penalty notice.
Minister of State for Public Health, Dawn Primarolo, said: "When we introduced the smokefree law last month, we predicted that it would be largely self-enforcing based on experience elsewhere and the fact that three-quarters of the public supported the move.
"These figures confirm that, just as happened previously in Ireland then Scotland, England saw very high levels of compliance in the first few days. All the signs are that businesses and the public have taken the new law in their stride.
"These high levels of real protection from secondhand smoke in public places and workplaces are a testament to everyone involved. Efforts from enforcement officers in local authorities and businesses, especially those in the hospitality sector and also the public have all contributed to making this country a healthier place in which to work and socialise."
The DoH also said there had been a steady downward trend in calls to the Smokefree England compliance line.
Amanda Sandford, research manager of the health campaigning charity ASH,added: "This is a fantastic response. As we predicted, the people of England have welcomed the smokefree law wholeheartedly. It has been largely self-enforcing because it is what the vast majority of people want. The smokefree law is working as intended: it is protecting people from toxic tobacco smoke and enabling people to work and socialise, free from the worst form of indoor air pollution."
The survey of enforcement authorities was conducted by Local Government Analysis & Research (LGAR). So far, data has been collected from 88,899 inspections, which includes 9,568 licensed premises.