You can read the whole thing here if you have a strong stomach. Note that the BMA explicitly views a fizzy drinks tax as 'a useful first step' but says that 'taxing a wide range of products is an important long-term goal.'
The BMA don't mention that their soda tax will cost the public £1 billion a year, nor do they acknowledge that it would be deeply regressive. Indeed, they want to make it more even more regressive by taxing fizzy drinks (which are disproportionately purchased by people on low incomes) and use the money to subsidise fruit and vegetables (which are disproportionately purchased by people on high incomes). Nice.
In the pages of The Guardian, their spokeswoman, Sheila Hollins, resorts to flat out lying...
“We know from experiences in other countries that taxation on unhealthy food and drinks can improve health outcomes, and the strongest evidence of effectiveness is for a tax on sugar-sweetened beverages."
Hollins is the BMA's chair of the board of science so must be aware of the evidence from countries that have experimented with taxes on food and drinks, including Denmark (which is also strangely absent from the pamphlet). The evidence on sugary drinks, in particular, is consistent in finding little, if any, change in patterns of consumption and no change at all in 'health outcomes', including obesity (see here and here for a summary).