More than 100 Lloyd's Names have signed up to a new Names association launched on Monday.
The Lloyd's Private Capital Association (LPCA) has pledged to protect the interests of private capital providers and seek redress if it found Lloyd's had failed to properly regulate the market.
Its first battle will be to prevent the Chairman's Strategy Group (CSG) proposals being voted through at the Lloyd's EGM on 12 September.
The new group is anxious about the future of private capital providers at Lloyd's, and their ability to recoup previous losses, if the market is converted to a franchise structure.
The LPCA has sent letters to 3,000 Names worldwide this week and is hoping to gain up to 500 members.
In the letter, LPCA chairman Mark Heywood said: "The resolution, if carried, is tantamount to a blank cheque to the council and corporation to act on the CSG proposals.
"Like me, I expect you will be rather reluctant to write such a cheque, and will want to show your discontent at the way you are being treated in no uncertain terms."
LPCA secretary Philip White emphasised that the association is not setting itself up in competition with other groups.
But instead it would look to co-operate with them where appropriate.
He also denied that it had been set up to join other groups in bringing litigation against Lloyd's.
However, he said legal action would be considered in future if other approaches failed, adding: "I always regard litigation as a point of last resort."
He said: "We thought a new era was dawning after Reconstruction and Renewal, and it appears that we are seeing a repetition of the past and its mistakes.
"If we have 400 to 500 Names behind us we will have an effective voice on the subject of the franchise and what compensation our members might receive if private Names are cut out of the picture."
The association, which will hold a meeting for its members next month, has signed up law firm SJ Berwin to advise it.