The BMA says a tough package of measures is needed to "tackle the soaring cost of alcohol-related harm" in the UK. It says the industry spends £800m a year on advertising and promotion.
But drinks industry bodies say alcohol advertising is already very tightly-regulated - and that education is crucial in curbing drink-related anti-social behaviour.
Huyton-based Halewood International is one of the UK's largest independent manufacturers and distributors of alcoholic drinks. Its brands include Lambrini and Lamb's Navy Rum.
Halewood's marketing director Graham Oak said: "The UK alcoholic drinks industry is highly competitive and as such it is not in our interests to produce marketing material that subsequently gets banned because this constitutes a waste of money.
"It is worth remembering that the sale and marketing of alcohol is already highly regulated in the UK. What we need is more effective enforcement of existing legislation combined with a centrally driven education programme rather than more rules and red tape.
"Many of the issues raised around the marketing of alcohol are based increasingly on perceptions and points of view rather than fact. For example it is suggested on a fairly regular basis that Lambrini is targeted at under age drinkers yet independent market research shows that 76% of people who buy Lambrini are over the age of 35."
Rae Burdon, chief operating officer of the Advertising Association, said:"The current rules regulating alcohol advertising in the UK provide a strictly-enforced framework for companies to communicate commercial messages responsibly in a mature and competitive alcoholic beverage market.
"Alcohol advertising compliance with the codes is extremely high and figures released by the Advertising Standards Authority as part of its pro-active monitoring of alcohol advertisements have revealed that 99% of them complied with the advertising codes."
David Poley, chief executive of the drinks industry social responsibility body the Portman Group, said: "The BMA is ignoring all the evidence that advertising causes brand switching, not harmful drinking. A ban would not improve our drinking culture and could even be counter-productive.
"The University of Sheffield found it would create fiercer price competition which could actually increase overall consumption. Lasting social change can be achieved only through sustained education accompanied by proper enforcement of the alcohol laws."
Wine and Spirit Trade Association chief executive Jeremy Beadles said: "The BMA says that it is not anti-alcohol yet with alcohol consumption falling since 2004 and Britain facing the worst recession since the 1930's they call for measures that would hit the pockets of millions of consumers and threaten the livelihoods of thousands of people working in the media, advertising, television, not to mention the drinks industry.
"Britain already has amongst the highest taxes on alcohol in Europe. It should be obvious by now that higher taxation and higher prices don't curb alcohol misuse. The drinks industry is funding a major campaign to change drinking patterns amongst young adults. We believe culture change is more likely to be achieved through long term education and tough enforcement."