Lloyd's chairman Lord Levene, giving his inaugural speech in the role, said last week that the market's US premiums were up 15% to a record $8.2bn (£5.1bn).
The US accounts for up to 40% of Lloyd's business and is its largest market.
Lloyd's specialist accountant Neil Coulson, of Littlejohn Frazer, said rates had risen to a similar degree on both sides of the Atlantic, but a reduction in some business classes, particularly liability, would limit profits in the UK.
"Although premium rates have increased very significantly on classes such as employers' liability, some people in Lloyd's have pulled back on those classes, so the total premium [in the UK] doesn't go up."
Coulson added that the shortage of EL cover was proof of the continuing hard market cycle.
"It highlights that in some areas people could find risk to write if they had more capacity and they could probably make a profit.
"But the market is presumably saying those are the areas it is least confident in and they are the last places it will put its capital."