Lloyd's is facing a credit crunch in November when syndicates need to scrape together money to support underwriting in 2003.
Heavy losses over the past three years will have drained many syndicates' coffers, leaving them short of cash.
Most market commentators forecast continuing profitable market conditions for underwriting next year, making it crucial for syndicates' long-term health.
But the cash shortage could restrict the market's capacity at a time when it needs to write more business to repair past losses.
Lloyd's specialist accountant Neil Coulson, a partner at Littlejohn Frazer, said: "A lot of the funding [of recent losses] so far has been using money that was effectively there already, rather than new money.
"If these people are going to write the same levels of business next year they are going to have to come up with more funds."
Coulson said a credit crunch could strengthen the hand of corporate members, whose backers are more likely to be willing to dig deep and fund capacity increases.
Syndicates relying more heavily on third party capital could lose out as a result.
Coulson said Names would face "further erosion of their position in the market" unless they were able to fund expansions.
He forecast the Lloyd's market would be able to increase its total capacity from its current £12bn - but said this growth could be at the expense of Names and syndicates needing their support, and more use of quota share agreements to boost underwriting.
"The market will probably grow overall, but only if the big boys can get the capital they want. Some of the big corporates won't be able to raise capital," he said.
"We will also find that the more mixed capital syndicates will be trying to attract Names and also do deals with new corporate backers.
"For anybody wanting to grow strongly, it's going to be tough."