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According to Michael Mosley, life expectancy rose through the Great Depression. In his Horizon programme Eat, Fast and Live Longer he claims:
From 1929 to 1933, in the darkest years of the great depression when people were eating far less, life expectancy increased by 6 years.
Since it seems strange to me that in four years life expectancy rose by 6 years, and that this happened just during Great Depression, can anybody confirm whether it is true?
While claim that life expectancy rose from 1929 to 1933 by 6 years is true, the conclusions are far fetched.
The effects of the Great Depression on the people didn't end in 1933. In fact for the people 1933 was the middle of the Great Depression. US unemployment rate has been constantly rising from 1929 until 1933, when it has peaked at 25% (source). So if you'd expect to measure the effect on people, it would be after 1933. And indeed, life expectancy fell by 1½ years 1933 to 1934, and reached local low in 1936 at 6 years less than 1933 (source). It did not recover to 1933 levels until 1938, which happens to be the year when unemployment reached pre-Great Depression levels.
A plot of above data (male and female life expediencies): 
In general, life expectancy is continually increasing.
http://mappinghistory.uoregon.edu/english/US/US39-01.html
Looking at the chart, you'll notice that life expectancy did indeed increase during the Great Depression, but at a lower rate than the previous and following decades.
