The percentage has increased every year since 1990, when it was 11.6 per cent.
The long-term rise in babies being born outside marriage or civil partnership has also continued, the ONS said, with 47.7 per cent of all babies in 2015 born outside marriage or a civil partnership, up slightly on the previous year.
The report said: "In most developed countries, women have been increasingly delaying childbearing to later in life, which has resulted in rising fertility rates among older women.
"This may be due to a number of factors such as participation in higher education and the labour force, the increasing importance of a career, the rising costs of childbearing, labour market uncertainty and housing factors."
A spokeswoman for the British Pregnancy Advisory Service, said the trend towards older motherhood was "here to stay".
"Rather than bemoaning this development, we should seek to understand and support the decisions women make," she said.