And almost half of them will be from low income and disadvantaged communities, widening the health gap between the haves and have-nots even further, say the authors.
The researchers draw their conclusions on an analysis of annual data between 1993 and 2004 from the Health Survey for England.
This samples a nationally representative cross section of households, and includes information on occupation and social class.
The analysis included almost 128,000 adults with valid weight and height measurements, from which a body mass index (BMI) can be calculated. A BMI above 30 denotes obesity.
The authors then calculated the likely prevalence of obesity by 2012, using three different approaches.
These included straightforward year on year increases, and assuming that the trends remain constant; allowing for a speeding up or slowing down in the rate of change; and linear trends for the six most recent years only.
Between 1993 and 2004, the prevalence of obesity almost doubled in men, from 13.6% to 24%, and rose by almost 50% among women from 16.9% to 24.4%.
On the basis of these trends, around one in three adults (32.1% of men and 33.1% of women) will be obese by 2012, equivalent to almost 13 million people.
Of these almost half (43%) will be among low income groups and manual social classes, while the prevalence of obesity among non-manual and higher income social classes will have climbed to 35%.
At the start of this decade, 9000 people met an early death every year as a direct result of obesity, and in 2002, at an annual cost to the English economy alone of around £7.4 billion.
"Trends in obesity among adults in England from 1993 to 2004 by age and social class and projections of prevalence by 2012"
Online First J Epidemiol Community Health 2008 doi 10.1136/jech.2008