They also want fast food outlets near schools and colleges, and pre-watershed TV advertising, to be banned.
The Academy of Medical Royal Colleges (AoMRC), which represents nearly every doctor in the UK, said the measures are necessary because obesity is the country's biggest health crisis.
The academy has released a report which calls on the Government, NHS and food organisations to take action to encourage people to eat a healthier diet.
The problem is especially acute in Scotland, where the most recent Scottish Health Survey claimed more than one in four people aged between 16 and 64 was grossly overweight. The survey, produced for the Scottish Government, warned obesity rates could reach 40% by 2030. Figures also suggest that 31% of Scottish children aged seven to 11 are overweight.
Professor Terence Stephenson, a paediatrician and chairman of AoMRC, said: "As health professionals, we see it across all our disciplines – from the GP's surgery to the operating table and everything in between.
"So it is no exaggeration to say it is the biggest public health crisis facing the UK today.
"It's now time to stop making excuses and instead begin forging alliances, trying new innovations to see what works and acting quickly to tackle obesity head on. Otherwise the majority of this country's health budget could be consumed by an entirely avoidable condition."
The AoMRC report criticises the present and previous UK governments for "insufficient and ineffective" attempts to tackle the problem and sets out 10 recommendations to stop the UK becoming the "fat man of Europe".
These include taxes of 20% on sugary drinks for at least a year, banning the advertising of foods high in saturated fat, sugar and salt before 9pm, and councils having the power to limit the number of fast-food outlets near schools and leisure centres.
Other recommendations involve NHS staff talking to overweight patients about their eating and exercise habits, surgery for the severely obese and advising new parents on how to feed children properly.
Professor Mike Lean, a human nutrition expert at Glasgow University's School of Medicine, said it was important to target children who were overweight before they went on to develop obesity. He said: "It has become such a huge issue we have the most senior medical professionals saying we have to do something about it."
However, Gavin Partington, director-general of the British Soft Drinks Association, said: "We share the recognition obesity is a major public health priority but reject the idea that a tax on soft drinks is going to address a problem which is about overall diet and levels of activity."