The number of women on company boards has almost doubled over the past four years to just under a quarter, marking "enormous" progress.
A target of 25% for this year, set by Lord Davies of Abersoch in 2011, is now close to being achieved, ministers believe, adding that 17 more women were needed to be appointed to FTSE 100 company boards to meet the figure.
The number of female senior executives has increased from 19.9% to 21%.
Lord Davies said the rate of change since his report had been "remarkable" and proved that the voluntary approach was working.
A study by the Cranfield University School of Management, published alongside the Government report, found there were 263 women directors in the FTSE 100, adding that the 25% target should be met before the end of the year.
The UK registered an increase of 12.6% in the number of women on top boards over the past decade and is now fifth in the world, said Cranfield.
Lisa Buckingham of the Institute of Directors said: "On current trends, the 25% target looks set to be reached this year, but this is far from the end of the debate. We need to focus on establishing the talent pipeline to increase the number of women in executive and senior management roles."