Ms McKeown said the ONS was seeing different patterns among age groups, adding "the increase in unemployment was driven mostly by younger people."
There was a quarterly drop in the number of people who were economically inactive because they were students or retired, but this was largely offset by a rise in economic inactivity for other reasons, including long-term illness and for other reasons.
Danni Hewson, AJ Bell's head of financial analysis, said the figures were creating "a clearer picture of a labour market that's soft, with younger workers facing the biggest challenges".
She said the decision by Chancellor Rachel Reeves to raise employer national insurance "made it more expensive for employers who had lots of part-time staff, many of them being younger workers dipping their toe in the labour market for the first time".
"The fact the ONS has found that the rise in unemployment in the three months to August was driven mostly by younger people suggests those warnings have become reality," Ms Hewson said.
"Making it harder to find these types of jobs could have a marked impact on their relationship with work in the future."
The ONS has said the unemployment rate should be treated with caution and it is taking additional steps to address concerns about the quality of the data.