Senior in-house lawyers have warned that law firms which fail to improve diversity within their ranks will lose out on work, with a call to arms to hold firms to account on improving female representation.

The issue was raised at the LegalWeek CONNECT conference yesterday (29 November), where a panel including Bupa group legal director Janet McCarthy, Serco GC David Eveleigh and Barclays head of external engagement Stephanie Hamon discussed how GCs can drive change within law firms.

Eveleigh revealed that last year he told one law firm that if it did not include partners in its gender pay gap reporting, he would no longer use it for work. The law firm subsequently complied after he spoke directly to the firm's senior partner.

The panel discussion, which was chaired by Obelisk Support CEO Dana Denis-Smith – the founder of the First 100 Years project, which charts the progress of women in law – also saw McCarthy issue a call to action to the lawyers in the audience to start conversations within their firms on this subject.

McCarthy – who joined Bupa last month from the Santa Fe Group, where she was chief legal officer – claimed that "law firms don't care about diversity unless their buyers do", and encouraged in-house lawyers with buying power to call out firms with sub-par female representation.

"I want to show young lawyers that it is possible to stand up and change the world today," she said. "I believe that if everyone starts that conversation, we can start a butterfly effect."

McCarthy said that at BUPA, "women reign", and she is among several women in senior management positions at the company, but added that she believes in-house legal departments do not need to be paragons of virtue on diversity themselves, to demand it from the law firms they use.

The panel also discussed what in-house lawyers can do to improve the gender balance within their own workforces and firms.

Eveleigh – who was last night named GC of the Year at the British Legal Awards – recalled attending an event held by several law firms, where a number of junior female associates approached him to request he start the conversation about improving gender balance with their senior partner.

He said: "You can support them by having that debate with their partners. I can use my buying power and also have those conversations."

Hamon agreed, saying the lawyers she works with often ask that she feed back to management about how important prioritising the subject should be.

She added: "It is easy to demonise law firms, but it's about positive reinforcement as well. We recognise that a challenge sits on our side too – it's about sharing best practice."

Hamon added that while the situation needs improvement, she believes people should be buoyed by the fact that the UK is making more progress on this issue than other regions such as continental Europe and the US.

She cited a particularly bad example demonstrated by one of Barclays' external law firms, which attended a meeting on how they were tackling the diversity issue "with a 60-page booklet and three men in their 50s".