The source of his concern was in nearby Lloyd's Avenue, where managers were trying to salvage the fortunes of 3,500 underwriting members whose affairs were once managed by the Gooda Walker agency.
They had just announced that losses had climbed to pounds 925m. For individuals in insurance syndicates, that meant an average liability of pounds 264,285 each. Since the bulk of the losses will have to be met from their private wealth, many face financial ruin.
The Lloyd's market as a whole is expected to report up to pounds 2bn worth of losses this year - on top of pounds 2bn in losses last year and pounds 500m in 1991.
Few financial institutions have suffered so big a loss over so short a time and survived intact. There has been widespread comment that Lloyd's, the oldest insurance market in the world, is close to 'meltdown'. In other words, not only are the members facing financial ruin, but Lloyd's itself might be facing bankruptcy.
Entering this troubled arena is Mr Rowland. He took over as chairman of Lloyd's at the beginning of last month but he has already created a small place in Lloyd's 305-year history. As the first paid chairman of the market, Mr Rowland, 59, will receive pounds 450,000 a year.
Previously, Lloyd's chairmen came from the companies that operated in the market and they returned to them after a two to four- year period in the job - with or without a knighthood for services rendered.
How did he feel about the losses now threatening to wipe out the generations of accumulated wealth of Lloyd's 20,000 members?
'I feel horrified but I cannot rewrite the past,' he said. 'What I am trying to do is to think about the future in such a way that it can benefit all members, and practical ways in which we can deal with the past. The losses are real. There is nothing I can do about that.'
That is cold comfort for underwriting members, forced to watch their wealth spent on the financial consequences of oil spills or transferred to American companies that have been sued successfully by former employees who have contracted the lung disease asbestosis.
Once again their anger is growing and after a series of stormy meetings with the Lloyd's authorities last year the members will be expecting positive action this year from Lloyd's new and paid chairman to provide them with financial relief.
The courts have been deluged with writs from those facing the largest losses. Some members have committed suicide. Last month a professional underwriter at Lloyd's was found dead with a gunshot wound in circumstances that the police do not regard as suspicious. An inquest takes place later this month.
Inevitably, any chairman of Lloyd's will be called to account by the members for the problems they now face, even though he was not leading the market when the troubles surfaced.
'I am not trying to avoid responsibility,' Mr Rowland said. 'We should all feel responsible for those losses in a proper sense.' He stressed that this statement did not suggest legal responsibility, obviously mindful of the minefield that he might get into.
'The fact that Lloyd's has brought benefit over generations is not much help to people who are suffering at the moment.'
How then can the members be helped? 'I cannot invent money. I cannot rub a magic lamp for money to appear from it. I try to explain what the situation is.'
There is, he says, no solution other than to try to increase Lloyd's resources through profitable trading in the future, to apply that profit to the members who have risked their own capital, and to strengthen the internal institutions within Lloyd's.
'I and my colleagues do not have the universal truth but we are trying to chart a course through difficult waters.'
In spite of the turmoil within Lloyd's, dramatic changes are being made in the style of management. Until comparatively recently Lloyd's was run like a club rather than a business. The lunches were good and the management was indifferent.
The management structure has been strengthened. In the past few months a dynamic chief executive, Peter Middleton, has been appointed at pounds 250,000 a year.
A former monk and diplomat, whose last job before joining Lloyd's was running the Thomas Cook travel agency, Mr Middleton has made a good impression among the underwriting members. He has persuaded them that he is looking for solutions to their problems and is anxious to head off further rounds of costly litigation.
On the regulatory front, Mr Rowland is supported by Brian Garraway, a former trouble- shooter at BAT Industries.
If Mr Middleton has struck a hopeful note among the members, Mr Rowland is more cautious about whether past troubles can be dispatched. By the end of April Mr Rowland hopes to have drawn up a business plan for the market, incredibly the first ever produced at Lloyd's.
'I am not suggesting that we will have an answer to every possible problem at the time. But we have a duty to explain how we are going to handle those problems and chart a route for the members in which they can have faith.'
Mr Middleton's brief extends to giving a strong lead to the hundreds of companies and executives that operate at Lloyd's.
'He does not have the right of instruction over competing companies in the market but he can provide an influence,' said Mr Rowland, who formerly headed Britain's largest independent insurance broker, Sedgwick Group.
The two men have yet to decide on their specific responsibilities in the new structure. 'We are assessing what our respective strengths are,' Mr Rowland said.
But it is perhaps revealing that both are keen to move their offices down from the marble halls of the 12th floor of the Lloyd's building to nearer where business is traded on the market.
Meanwhile Mr Rowland wants new capital brought into Lloyd's. In a report on the market's future last year, he recommended that not only individuals but also companies, and particularly insurance companies, should be allowed to invest in Lloyd's.
'It would be unwise in the present situation to bank on our future capital being provided by individuals,' he observed.
So in the future he wants market forces to 'produce a framework for incorporated capital, a fair structure which will have the support of all members'.
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