The row is about the way Mr Rowland, who became chairman at the beginning of this year, has taken on more of the daily running of Lloyd's and the planning of reforms. Mr Middleton, an outsider who took up his post as chief executive last September, is increasingly sidelined in an ambassadorial role overseas.
Insiders fear that the mounting tension between the two could undermine efforts to find crucial new sources of finance to save the market from collapse. Last week, Lloyd's reported losses of pounds 2.9bn for the 1990 underwriting account, the worst in the market's 305-year history. Next year, it is expected to show losses of at least pounds 1bn, making a total over four trading accounts of more than pounds 6bn.
Those anxious to see changes at Lloyd's also fear that Mr Rowland's growing power as chairman is another example of Lloyd's insiders keeping control by undermining the power of outsiders brought in to improve the workings of the market.
'Officially they say things are fine, but the two men are so different that there are bound to be clashes,' said one senior member of the Corporation of Lloyd's, the market's administrative hub.
Mr Middleton, 52, is a gritty businessman who successfully ran the Thomas Cook travel agency before he joined Lloyd's on a salary of pounds 250,000. Mr Rowland, 60, has spent his entire career at Lloyd's and headed Britain's largest independent broker, Sedgwick Group, before he became chairman on a pounds 450,000 salary.
At last week's results presentation, Mr Middleton was not involved to the same extent as he had been at a meeting in May to introduce Lloyd's plans for the future.
Mr Middleton spends much of his time travelling. Since last September he has been to America, South Africa, New Zealand, Australia and Canada trying to reassure Lloyd's large overseas membership and those companies which provide it with business that the market is still viable.
'Mr Middleton is trying to make up for the neglect of the capital base - the market's underwriting members,' said one insider.
By contrast, Mr Rowland spends most of his time at Lloyd's, surrounded by advisers as they draw up plans to introduce new money in the form of corporate capital.
The rift between Mr Rowland and Mr Middleton opened up early in the relationship. Mr Middleton had hoped an extensive range of financial aid could be provided for the hardest-hit underwriters, 17,000 of whom are suing Lloyd's.
But Mr Rowland decided that only limited help could be given in view of the seriousness of the problem.
Relationships between chief executives drawn from the business world outside Lloyd's and an internally appointed chairman of the market have always been tense. Some experts believe the rift carries echoes of the clash between Ian Hay Davison, the first outsider brought in as chief executive of Lloyd's to reform the market, and Sir Peter Miller, the chairman and a Lloyd's insider, which led to Mr Davison's departure in 1985.
Many of the names facing massive personal losses and possible bankruptcy already believe that Mr Rowland's appointment as chairman has not stopped Lloyd's insiders closing ranks against accusations of incompetence and fraud from outside the market.
Jeremy Warner, page 2
Men who lost a billion, page 13
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