Married couples saw a drop of four per cent to 12.1 families in the same period, however, the ONS said the obvious conclusion of a shift towards non-married couples was not necessarily the case.
However, the ONS said that the increase in cohabitation did not fully explain the decline in marriage, because the research found fewer women aged between 25 and 29 were forming any union, either marriage or cohabitation, before the age of 25.
"This suggests a delay in partnership formation for younger generations of women," the Telegraph quoted the report.
The report further pointed out that the decline of the married family and the rise of cohabitation could have a negative impact on health, as the offspring of married couples tend to be healthier than those of single mothers, and do better at school than those whose parents are separated or cohabiting.
"Partnership continues to be the healthiest state in general. There are health benefits associated with partnership, especially marriage, but there are variations by sex," the report said.
"In particular, older single women have better health then married women on many indicators of health status," it added.
Meanwhile, the research found single parents increased by 8% to 2.6 million, with single mothers tending to be younger than their male counterparts.
The study, which includes forecasts from Government actuaries, predicted a 250 per cent increase by 2031 among people aged 45-64 who cohabit.
The study, which includes forecasts from Government actuaries, predicted a 250 per cent increase by 2031 among people aged 45-64 who cohabit