A further 500,000 are in cohabiting step-families, and 400,000 in married step-families.
The analysis said cohabiting women over 35 are 58 per cent more likely to have a child than wives of the same age.
Their numbers have grown by 600,000 since 1999, the ONS said.
The increase in children of broken homes came during the years when the Labour government maintained that all family types are equally good for children and the benefit system was re-shaped to reward single parents and penalise couples.
Britain now has one of the highest birth rates for older women in the world, with 3.8 per cent of babies born to mothers over 40.
Children face an unprecedented scramble for primary school places following forecasts that pupil numbers will rise by more than 500,000 in only eight years.