Highway Insurance managing director Andrew Gibson claims operating in Lloyd's is "too expensive" and that the "administration too burdensome".
Like others who are finding Lloyd's regulation too onerous, Gibson is seeking to do more business outside the market.
"There are three main reasons we are seeking to do more business outside Lloyd's: because it is cheaper; because we are not connected to the Central Fund and because the administration is less burdensome," he said.
"The Lloyd's administration creates serious costs. I estimate it costs hundreds of thousands of pounds per year," he added.
Gibson said the current trend of regulatory requirements increasing may continue, adding: "The amount of returns we have to complete has grown dramatically in the last five years."
A Lloyd's spokesman said: "Lloyd's has committed itself to cutting the cost of doing business in the market. Work to do this began in the late 1990s and we have seen year on year cost reductions, only hindered by 11 September.
When asked if future franchise arrangements, proposed by the Chairman's Strategy Group, would mean more administration he said: "We are conscious of all these issues and will not simply burden people with more paperwork."