Established by William Almack in 1765, these fashionable assembly rooms in King Street, St James, were at the centre of late eighteenth century London social life for the rich. The guests lists were controlled by seven high ranking ladies, and as the Irish poet and wit Henry Luttrell (1766-1851) noted, banishment was a grave penalty:

All on that magic List depends;

Fame, fortune, fashion, lovers, friends;

'Tis that which gratifies or vexes

All ranks, all ages, and both sexes.

If once to Almack's you belong,

Like monarchs you can do no wrong;

But banished thence on Wednesday night,

By Jove, you can do nothing right.

The Assembly Rooms provided gambling and supper, and all-night dancing. Supper was served at 11 pm, at which time the doors were closed to members and guests. The Rooms had a strict dress code and gentlemen had to wear knee breeches and a white cravat. The Duke of Wellington was refused entry for wearing trousers. 

The committee worked on a rotation system, one lady assuming the role of patroness. In 1814, the committee comprised:

• Lady Sarah Jersey.A leading London socialite
• Lady Emily Cowper. Daughter of the 1st Lord Melbourne, Emily Mary Lamb married the 5th Earl of Cowper on 21 July 1805. Two years after the Earl's death in 1837, Lady Sarah married the 3rd Lord Palmerston. 
• Lady Sefton
• Princess Esterhazy. Princess Theresa of Thurn and Taxis married Prince Esterhazy, the Austrian Ambassador. Countess Lieven described her as "small, round, black, animated, and somewhat spiteful."
• Countess Lieven
• Mrs. Drummond-Burrell. Later Lady Willoughby de Eresby.

(See Gronow's description below). Members of Almack's were permitted to bring a guest, if that guest passed the personal scrutiny of the patroness, who granted a "Stranger's Ticket" if she approved of the guest.

Lord Melbourne's first wife, Lady Caroline Lamb had been barred from Almack's by Lady Jersey after she was scandalously portrayed in Lamb's novel, Glanavon, depsite an appeal to the Duke of Wellington for re-admittance. (Young Melbourne)

The popularity of the Rooms declined from 1835, and balls ended in 1863. 

Captain Gronow on Almacks

In the year 1814, my battalion of the Guards was once more in its old quarters in Portman Street barracks, enjoying the fame of our Spanish campaign. Good society at the period to which I refer was, to use a familiar expression, wonderfully "select." At the present time one can hardly conceive the importance which was attached to getting admission to Almack's, the seventh heaven of the fashionable world. Of the three hundred officers of the Foot Guards, not more than half a dozen were honoured with vouchers of admission to this exclusive temple of the beau monde; the gates of which were guarded by lady patronesses, whose smiles or frowns consigned men and women to happiness or despair. These lady patronesses were the Ladies Castlereagh, Jersey, Cowper, and Sefton, Mrs. Drummond Burrell, now Lady Willoughby, the Princess Esterhazy, and the Countess Lieven.

The most popular amongst these grandes dames was unquestionably Lady Cowper, now Lady Palmerston. Lady Jersey's bearing, on the contrary, was that of a theatrical tragedy queen; and whilst attempting the sublime, she frequently made herself simply ridiculous, being inconceivably rude, and in her manner often ill-bred. Lady Sefton was kind and amiable, Madame de Lieven haughty and exclusive, Princess Esterhazy was a bon enfant, Lady Castlereagh and Mrs. Burrell de tres grandes dames.

Many diplomatic arts, much finesse, and a host of intrigues, were set in motion to get an invitation to Almack's. Very often persons whose rank and fortunes entitled them to the entree anywhere, were excluded by the cliqueism of the lady patronesses; for the female government of Almack's was a pure despotism, and subject to all the caprices of despotic rule: it is needless to add that, like every other despotism, it was not innocent of abuses. The fair ladies who ruled supreme over this little dancing and gossiping world, issued a solemn proclamation that no gentleman should appear at the assemblies without being dressed in knee-breeches, white cravat, and chapeau bras. On one occasion, the Duke of Wellington was about to ascend the staircase of the ball-room, dressed in black trousers, when the vigilant Mr. Willis, the guardian of the establishment, stepped forward and said, "Your Grace cannot be admitted in trousers," whereupon the Duke, who had a great respect for orders and regulations, quietly walked away.

In 1814, the dances at Almack's were Scotch reels and the old English country-dance; and the orchestra, being from Edinburgh, was conducted by the then celebrated Neil Gow. It was not until 1815 that Lady Jersey introduced from Paris the favourite quadrille, which has so long remained popular. I recollect the persons who formed the very first quadrille that was ever danced at Almack's: they were Lady Jersey, Lady Harriet Butler, Lady Susan Ryder, and Miss Montgomery; the men being the Count St. Aldegonde, Mr. Montgomery, Mr. Montague, and Charles Standish. The "mazy waltz" was also brought to us about this time; but there were comparatively few who at first ventured to whirl round the salons of Almack's; in course of time Lord Palmerston might, however, have been seen describing an infinite number of circles with Madame de Lieven. Baron de Neumann was frequently seen perpetually turning with the Princess Esterhazy; and, in course of time, the waltzing mania, having turned the heads of society generally, descended to their feet, and the waltz was practiced in the morning in certain noble mansions in London with unparalleled assiduity.

Sources

Weinreb; Gronow.