'Let's just say that he could have made a better start,' said a key figure at one of the main securities houses last week.
Mr Lawrence's critics, none of whom wished to be named publicly, do not doubt his intellectual and managerial abilities.
However, they question whether he has the right manner and personal qualities to lead the Stock Exchange as it tries to recover from the disasters of the past few years. Morale has been low for some time at the Exchange, and some people in the City have challenged its very existence.
''Nobody questions his mind, but part of this job is the art of persuasion,' said one highly placed City source. 'And what the Exchange needs right now is somebody who works away like a black (sic) at gaining the support of member firms,' he said.
The grammar-school-educated Mr Lawrence joined the Exchange from the Prudential, where he was finance director. He is therefore considered an outsider in the public-school- dominated City, despite the clout the Pru wields as the country's biggest investor. But he has not helped his cause in the City by missing functions at which he was expected.
A leading City source recalls an informal gathering at the Stock Exchange Tower attended by many of the securities houses' leading players.
'We were told that he would be there,' said the source, 'and he just didn't show up. When you get all the kings in the City in the Tower at the same time, one would expect the new chief executive to make a big attempt to get there, too.'
Recently, Mr Lawrence missed the Exchange's annual general meeting, the board meeting before that and also a party for the outgoing chairman, Sir Andrew Hugh Smith.
'Whatever happened, he should have been here,' said a senior source. 'It was tactless, to say the least.'
Mr Lawrence was on a previously arranged boating holiday in the Mediterranean.
A Stock Exchange spokeswoman suggested that the Exchange's annual general meetings were traditionally low-key affairs, lasting around five minutes. She also said that the outgoing chairman had had about five separate leaving occasions and that Mr Lawrence had been at most of them.
She said that Mr Lawrence had been involved in a number of 'frank discussions' with people both inside the Stock Exchange and with its member firms. 'He puts problems to them and sees how they respond,' she said. Another spokeswoman added that 'he had spent much of his time going out to the market, speaking to people, trying to get practitioner input.'
Stock Exchange insiders are hoping that Mr Lawrence will gain greatly from working alongside John Kemp-Welch, the new chairman, who has been in the job just a few days. Mr Kemp-Welch is widely admired in the City and is expected to strive hard to restore the Exchange's credibility and repair its damaged relationship with the Bank of England, which soured after the Taurus affair.
'I am sure the City will give Lawrence a second chance and see how he works alongside Kemp-Welch,' said the senior City source, raising his eyebrows knowingly.
Mr Lawrence declined to be interviewed.
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