LONDON, June 23 (Reuters) - Britain's six-year drive to increase the number of women in senior management at financial firms is "stagnating" for the first time, a review for the finance ministry said on Thursday.

The ministry launched its voluntary Women in Finance Charter in 2016 and more than 400 firms have now signed up.

A review by New Financial think tank found that 78% of signed-up firms are meeting or are on track to meet their targets, up 5% on last year. 

The average level of female representation in senior management remained flat at 33% in 2021 compared with 2020, the review said.

Almost half of firms have committed to have 40% of their boardroom made up of women.

"I am concerned to see progress stagnating," Women in Finance Champion Amanda Blanc said.

"Frankly, up to now there has been too much tinkering at the edges and not enough fundamental change," said Blanc, who is also chief executive of insurer Aviva.

"There are some glimmers of hope with more ambitious targets being set and met. But for the sake of women, companies and society, we’ve got to work quicker and harder."

Signatories agree to support the progression of women into senior roles by setting targets to improve diversity and publicly report on their progress.

"I welcome this year’s progress, but settings targets is just one part of the process – I am today calling on firms to double-down on their to commitments and continue to deliver greater gender-equality in the workplace," Britain's financial services minister John Glen said in a statement.