Escorts in Berkeley Square, W1J, as the Society arranges them after dark

The square was laid out in the 1740s across the upper gardens of Berkeley House, the mansion on Piccadilly that lent it a name and, by covenant, kept its northward view open. For much of the next two centuries its best known address belonged to a confectioner. At Gunter's, on the eastern side, waiters threaded through the traffic with ices for ladies who stayed in their carriages beneath the trees, and a lady might sit there with a gentleman without a word said about it. Service in public, and no questions asked: the square acquired the habit early and never gave it up.

The houses keep their own counsel. Number 44, on the west side, has a staircase by William Kent that architectural historians still ask to see. Annabel's opened in its basement in 1963 and has since moved next door to number 46, where members and their guests dine behind a Georgian front that gives nothing away. Off the north-east corner, Bruton Street has a distinction of its own: a future queen was born at number 17 in April 1926.

The people who write to Cressida from W1J are mostly here on business that never reaches the newspapers: senior people from the investment houses that keep offices around the garden, collectors between sales, guests in the Stratton Street hotel for a week of meetings. What they ask for rarely varies. A table that is hard to get, a companion who can talk to anyone seated at it, and an evening that ends as quietly as it began.

Guests near the square usually stay at one of five hotels. The Society has no understanding with any of them; they are named the way an invitation names a house, so that you know where the evening starts. Your companion arrives as your visitor, and a lobby sees nothing more than that.

Closest to the garden is the big house at W1J 8LT, a walk of two or three minutes south to Stratton Street. King George V opened it in 1927, and its lobby stays busy until late, which suits an arrival that should go unremarked. A quieter townhouse at W1J 5EB lies a few minutes west along Charles Street, smaller in scale and easier at the door. W1J 7BH, on Half Moon Street, sits between Curzon Street and Piccadilly, four or five minutes away. We give the address rather than the name.

Two grander houses are a short walk further. W1K 2AL, on Carlos Place, is reached along Mount Street in about six minutes, and the dining room Hélène Darroze runs inside it is reason enough for many guests to stay there. The old house at W1S 4BP is three or four minutes east on Albemarle Street, where the English Tea Room serves until early evening and the bar carries on well after it.

By Underground, the square has three stations in reach. Green Park, which serves three lines at once, the Victoria, the Jubilee and the Piccadilly, lies about four minutes down Berkeley Street. Six minutes' walk north, Bond Street brings the Central and Jubilee lines together with the Elizabeth line from Heathrow. Hyde Park Corner, a stop on the Piccadilly line alone, takes nearer ten minutes, by way of Curzon Street and the backs of the Park Lane hotels.

Your companion does not take the Tube. A car brings her to the door, and within Zones 1 and 2 its fare is the Society's affair. For a request made in the evening, allow about an hour from Cressida's confirmation to the knock, more when Berkeley Street jams at seven or on Fridays; the exact time reaches your thread as the car pulls away. An evening settled during the afternoon arrives at the minute you chose.

Cressida asks one thing before your companion sets out: whose name the room carries and which number it is, or, for a flat or a house, the street and the door. There is no second round of questions. The fee is settled between the two of you when she walks in, and nothing is added afterwards. The booking page sets out each step in order.

Suppose a guest whose day went on meetings in an office overlooking the garden. At six he writes to Cressida: a table for two at half past eight, company from eight, his hotel on Stratton Street. By seven he has a name, Angelika, and a figure, the dinner date, four hours, £1,800. She reaches the hotel bar before he does, in a single strong colour, and has already chosen the corner.

Dinner is a few minutes' walk away, in a small room on Bruton Place whose menu has stayed the same for years and is expected to stay that way. They talk about the painting she stood in front of that afternoon and the deal he did not close. At eleven they cross the garden under the plane trees, past the dark front of number 44, and take a last drink back at the hotel. She leaves at half past twelve. The square is empty except for a taxi waiting for somebody else.

Three companions give Mayfair as their home district, and so reach the square first. Angelika plans her evenings around a private view and a late trio. Luna, unmistakable with her dark auburn hair, would rather choose the wine herself and keeps Monday to Thursday for guests. Samanta, tall and composed, likes a dinner fixed by teatime and notices the lighting in any room before you do.

A little further out, Liana and Rosa come down from Marylebone, across Oxford Street. From Knightsbridge, Bianka and Sonya cross by way of Hyde Park Corner, and Violetta comes up from Belgravia when she is in town. The rest of the circle travels to W1J just as readily.

From the garden, three short walks lead to the Society's other pages. Go south down Berkeley Street and within five minutes you are among the hotels and dining rooms of Piccadilly, W1J 9BR on the corner. Head west along Charles Street and Mount Street into the rest of Mayfair, where the Brook Street and Carlos Place houses hold their end of the district. Keep going and the side streets give out onto the traffic below the tall hotels of Park Lane, with Hyde Park dark beyond them.