Names have expressed concern over plans by the Financial Services Authority (FSA) to slash the number of shares Lloyd's investors can hold in one company.
Those with holdings over the limit will have to dispose of their excess shares and could incur huge capital gains tax liabilities.
The proposals were laid out in the Lloyd's rule book, published two weeks ago, and are set to be enforced by January 1, 2003.
Private and corporate Names will only be allowed to keep 5% of their assets in a single firm – a steep drop from current limits of 20%.
Under the Financial Services and Markets Act, by November 30, 2001 the FSA will have the power to tighten up Lloyd's Market practices.
The new legislation aims to prevent the equity of Lloyd's fluctuating if a firm's shares plummet on the stock market, as has happened to some internet technology stocks.
Lloyd's spokeswoman Deborah Fowler said: "We want to make sure there is not a reliance on one company. This is beneficial to the integrity of our resources."
But private investors at Lloyd's annual meeting last Friday said they were worried about the rules and how shares in unit and investment trusts would be assessed.
Lloyd's has now written a letter to the FSA, outlining some of its fears and asking the body to consider allowing a transitional period to enforce the rules.
"We have always had an interest in asset concentration rules and support the principles of spreading risk," said Lloyd's finance director Andrew Moss. "It's just a question of how you implement it.
"We would like to spread that change over a period of time, rather than have it all come in on one date.
Lloyd's is pushing for a 2006 deadline for Names and individuals with less than £3m of funds so they can manage their tax affairs.
Fowler confirmed unit trusts and other collective investments would not be included in the share limit.
There are currently just under 3,000 individual Names and around 800 corporate capital providers in Lloyd's.