In a statement issued at the weekend, Mr Treger called on the management of Countrywide Assured, which is valued at pounds 379m, to announce a pounds 50m share buyback, to be funded by borrowing as the company has a "minimal" level of debt.
He also urged the separation of the life insurance and financial services divisions in order to improve valuation. The financial services arm rests on distribution through the Hambros Countrywide estate agency network.
Countrywide's new insurance business has grown rapidly, but the two separated divisions could secure their flow of business if necessary with a marketing agreement, according to the proposal.
The statement noted that Countrywide Assured is valued at 8.5-times earnings, or nearly pounds 400m, compared to a multiple of 23.1 for comparable insurance companies.
"The creation of two separate businesses will, we believe, give the market the transparency it needs to achieve the right valuation," it said.
John Mansfield Group, the bidding vehicle of Mr Treger and Mr Myerson, launched a hostile takeover bid for Marley, the building materials group, at the end of last month.
The bid was withdrawn last week after a higher offer was accepted from the Belgian building materials group Etex.