Fox was commenting on figures released this week by Acas that show 17,145 people used the early conciliation service from its introduction on 6 April to the end of June.
The service, intended to lessen the amount of tribunals by settling disputes between employers and their staff early, was voluntary in April. During this month about 1,000 people contacted Acas about their cases.
When it became mandatory in May the figure jumped to 1,600 and was similar in June.
Fox told HR magazine the scheme has had an "encouraging start". He suggested that if the success continues, the effect of "relieving pressure" from the tribunal system may mean the government looking at the level at which they set the tribunal fees.
The fees were introduced last October. For an individual to bring a claim against their employer, it currently costs between £160 and £250, depending on the type of case raised.
Fox said if early conciliation continues to be a success the government might consider "taking its foot off the accelerator" on fees.
"Fees were initially introduced as a way to lower the number of cases brought and relieve pressure on the tribunal system," he said. "Early conciliation is perhaps a better way to do this.
"The government possibly overcooked the fees when they were brought in. The level seemed high to employers and experts alike. If the numbers keep coming down through early conciliation it could mean them reviewing their options."
Discussion over legal action
CIPD employee relations adviser Mark Emmott welcomed the news that early conciliation is apparently helping people to resolve disputes without reverting to tribunals.
"Although these figures don’t allow firm conclusions to be drawn about the impact on claims volumes, it looks increasingly possible that early conciliation will transform the process of dispute resolution by encouraging employers and employees to resolve issues by discussion, rather than by legal action," he said.
Irwin Mitchell employment partner Fergal Dowling pointed to figures that suggest only 7% of staff and 9% of employers have rejected the offer of early conciliation.
“These statistics point to a positive start for early conciliation. It is too early to judge what the impact will be on the future numbers of employment tribunals, but employers will no doubt be encouraged and welcome these findings," he said.