A 17.5% rise on fatty, sugary or salty food would cut heart and stroke deaths by 1.7%, the study in the Journal of Epidemiology and Community Health said.
One of the researchers declared the time was right to debate a "fat tax".
But the idea was dismissed in 2004 by former prime minister Tony Blair as too suggestive of a "nanny state".
The researchers from the Department of Public Health at Oxford University are among the first to try to work out how targeted taxes might have an effect on levels of illness. hey used economic data first to work out how demand would fall as the price of unhealthy foods increased, and which foods people might turn to instead - then used these results to predict the benefit on the health of the population.
Initially at least, average weekly food bills would increase by 4.6% per household.
Change for the worse
They first applied the tax only to dairy products containing high levels of saturated fats - such as butter and cheese, as well as baked goods and puddings.
However, their analysis found that people would simply switch over to other unhealthy foods such as those containing high levels of salt, perhaps even increasing the risk of stroke and heart disease.
They then turned to a different measure of food "healthiness" called the SSCg3d score, where points are awarded for the content of eight nutrients in 100g of the food.
Taxing all products which scored poorly on this scale saved lives, they said, with approximately 2,300 fewer deaths a year from heart disease and stroke.
Finally, they tweaked the range of taxed products to include those foods which might not score so poorly on the scale, but may be used as alternatives if unhealthier foods were taxed.
This resulted in small additions to the list of taxed and untaxed foods to encourage healthier eating.
This approach yielded the most apparently striking results, with as many as 3,200 deaths prevented.
Dr Mike Rayner, who worked on the study, said that the third, seemingly most effective, option was "more theoretical", and less practical to implement, but called on government to consider taxing high scoring foods.
He said: "This is still at a fairly early stage, but the time is right for more debate on the issue of 'fat taxes'.
"The other thing which would have to be done is to look at the possibility of subsidies for healthier foods, rather than simply looking at increases in tax."
'Nanny state'
However, Maura Gillespie, from the British Heart Foundation, said that it did not yet support "fat taxes".
"The debate on unhealthy diets is important as it is estimated that 30% of deaths from coronary heart disease are caused by unhealthy diets.
"Further evidence is needed on the effect of targeted food taxes before we can support a 'fat tax'."
When Downing Street's strategy unit was reported to be proposing fat taxation in 2004, Tony Blair said that such a move could actually turn people off the idea of healthy eating.
He told a Labour Party Big Conversation event: "People don't want to live in a nanny state."