I dunno about that.
The evidence I've seen is that inequality was at its lowest during this period and that there is a correlation between equality and mobility.
So, whilst it's reasonable to suggest that social mobility might have been at its highest then, but I wouldn't assert it with 100% confidence.
Flicking through Piketty yesterday (flawed as it is) he seems to suggest that wealth/income gaps can narrow without increasing social mobility.
Personally, I would hypothesize that for sections of the population (predominantly the newly created lower m/c) there was greater mobility available because of free University education, expansion of professional occupations etc. But I'd be hesitant to generalise this across society.