Likewise, four times a year the Holden Lodge meets at Freemasons Hall, an imposing stone building east of Covent Garden. Again the common link is their employer, this time Midland Bank. Soon after, their Masonic counterparts at National Westminster get together.
There is nothing unusual about these meetings. Up to 300,000 men are estimated to be Freemasons. Many are financiers and businessmen. There are more than 8,000 lodges, some of them exclusive to a particular employer or industry. Lloyd's, the insurance market, famously has three, including the Lutine Lodge.
Share traders have several lodges. One is said to be the Verity, whose members congregate at the City of London Club in Old Broad Street, conveniently close to the old Stock Exchange tower, on the first Thursday of February, October and December. The Bank of England also has its own lodge.
While Freemasonry in the police, the judiciary and local government has been the focus of opposition and suspicion, Masons in the business community have escaped largely unscathed.
However, a dispute in the John Lewis retail group illustrates how resentment of Freemasons is still rife. It also threatens a wider embarrassment for 'the craft', which nowadays is trying to foster a more open and less sinister image.
The trouble began three months ago, when Stuart Hampson, the deputy chairman of John Lewis, publicly admitted he was a Mason, in the staff magazine. The question had been put to him and he decided to do the honourable thing and disclose his Masonic links.
Referring to 'the widespread popular belief that the organisation is embroiled with improper favours, preferential advancement of its members and unethical business practices,' he said he had never encountered such behaviour.
Mr Hampson, who takes over as chairman in February, also divulged he had been a Mason for more than 25 years. A former civil servant - he served Roy Hattersley, Sally Oppenheim and John Biffen - Mr Hampson considered the best thing was to come clean.
But his honesty seems to have backfired. There has been unremitting criticism of his Freemasonry (and some support) in the letters column of the magazine. John Lewis, which takes in department stores and Waitrose supermarkets and which last week reported falling interim profits, is a workers' co-operative with about 34,000 staff or 'partners'. Uniquely, the magazine provides a real forum for debate and complaint, because correspondents may write in anonymously. It is not just a propaganda sheet.
To that extent the John Lewis experience probably reflects what is felt - but rarely voiced - in other less democratic businesses, where to condemn the Masonic boss publicly is to commit career suicide. Whatever the facts, there is a common suspicion that Masons look after their own, putting allegiance to fellow Masons ahead of responsibility to their shareholders, colleagues or customers.
Some John Lewis staff have called for Mr Hampson to resign from the Freemasonry or quit John Lewis.
One staff member demanded that all senior managers should state whether or not they were Masons, otherwise fears of 'a creed of mutual self-advancement' would persist. Apart from the present chairman, Peter Lewis, who has denied ever being a Mason, none of the senior managers has responded to this challenge.
Mr Hampson says he has to grin and bear the protests: 'It's a bore. There will always be some people who think there is something sinister.' But he has no regrets about coming out of the closet. 'Total honesty is essential.'
He sees a distinction between the chairman, who has to be open, and other senior managers, who do not. 'I don't want everyone declaring themselves. I don't want to know.
'I don't see why Masons should declare themselves any more than members of the MCC or the Catholic Church.' However, he admits that several of his staff have indicated to him that they are fellow Masons since the row began.
Mr Hampson's views are echoed by other Masons. Sir John Banham, the former director-general of the Confederation of British Industry, sees his Freemasonry as 'a complete irrelevance' to his professional life. 'I've been a Mason I suppose for 20 years or so, and not once in those 20 years can I recall an occasion when business was even discussed.'
Sir John, who is listed in the Masonic Year Book as a senior grand deacon of the United Grand Lodge of England, says: 'I think it's a private matter. I've never known there to be any hint of improper conduct. As a former head of the Audit Commission, this is something I look at very carefully indeed.'
He also denies that Masons face a potential conflict of interest because of the oath of loyalty they are thought to swear. 'That's a load of baloney. I never swore any allegiance to that effect.'
However, Martin Short, author of Inside the Brotherhood, believes the Freemasonry can be more sinister, especially in the City, where there are hundreds of lodges. 'The Square Mile has been squared, and encompassed, many times over by the men in lamb-skin aprons. The capacity for corruption is there. It is a kind of additional old boy net. I think it blurs people's objective edges.'
He points to one lodge he came across in his research, where the members were largely made up of Ministry of Defence procurement staff, Army officers and senior managers of armaments manufacturers. 'Nor was Masonry a force for good in the Lloyd's insurance scandals,' he adds.
The Labour MP Chris Mullin is also suspicious of Masonic lodges and other secret societies. His Private Member's Bill, to be debated in November, calls for public figures to be obliged to disclose membership.
According to the current draft, that would also apply to managers of some private companies, such as British Steel and the electricity utilities.
According to Ken Helps, assistant to the Grand Secretary at the United Grand Lodge of England, businessmen are given no advice on the matter: 'We leave it purely up to them. They are completely at liberty to disclose if they want. But they must not use Freemasonry to improve their business or professional occupation.'
Although most businessmen keep their Freemasonry secret, a few openly admit it. Sir Michael Richardson, chairman of the stockbroker Smith New Court and adviser to many powerful businessmen including Lord King and Lord Hanson, is one.
In the mid-1980s, when Sir Michael was managing director of N M Rothschild, he tried unsuccessfully to sell the Royal Masonic Hospital in Hammersmith against the wishes of the many rank-and-file Masons, in a celebrated battle that ended in the High Court.
Lord Farnham, chairman of the Provident Mutual insurance group and a former chairman of the merchant bank Brown Shipley, is Pro Grand Master, and therefore second only to the Duke of Kent in the Masonic hierarchy. Lord Lane of Horsell, the former senior partner of the accountancy firm BDO Binder Hamlyn, is another prominent Mason.
But most Masons remain tight-lipped, revelling in the mystery. And this is Catch-22. For however harmless most Freemasonry may be, it will never shrug off its sinister image while it remains secret.