Blake Nixon, a director of GPG, said shareholders had lost faith in Staveley's management. "The company has lurched from one management crisis to another," he said.
"After two or three complete reorganisations it is still not working. Something needs to change."
GPG takes an uncompromising stance towards underperforming investments. The group is currently embroiled in a pounds 42m hostile bid for Bluebird Toys, the Polly Pocket and Plasticine company, which it launched after becoming frustrated with Bluebird's falling share price.
GPG has also been aggressively building a stake in Staveley. Last month, the company bought another 13.2 million shares, taking its shareholding to 11.3 per cent and making it the second largest shareholder behind Schroders, which has 17 per cent.
Staveley shares have dropped by a third since June. In the past five years, they have halved in value.
GPG is unlikely to put any direct pressure on Staveley until the Bluebird Toys bid is over. But any action is likely to win support from Staveley's other major shareholders, which include Britannic Assurance and Prudential.
In January last year, Staveley issued a profit warning after Chronos Richardson, its industrial measurement subsidiary, ran into problems in Italy and France.
The group subsequently announced that it had put Chronos and Weigh-Tronix, its other measurement business, up for sale in order to concentrate on building up its engineering and business services arm.
"Staveley's management decided that because they'd failed something had to go," said Mr Nixon.
"So they decided to sell the business and keep the management."
A sale of the measurement division is thought to be imminent. But investors are likely to oppose any attempts by Staveley's management to reinvest the proceeds, preferring them to hand the cash back to shareholders.
GPG also wants the company to consider a demerger of British Salt, its profitable subsidiary which has a near monopoly on the UK salt market. The company, which this year is expected to make profits of pounds 13m-pounds 14m on sales of about pounds 35m, generates a steady flow of cash.
A spokesman for Staveley said the company's directors were looking at ways of maximising the returns to shareholders.
Mr Nixon, however, remains uncompromising, pointing out that Staveley's board was paid pounds 1.5m last year - almost pounds 600,000 of which went to chief executive Roy Hitchens - while the directors have no significant equity stake in the business.Reuse content