In British-English slang, the noun muslin was used to designate women regarded collectively as objects of sexual desire. In particular, the phrase a bit of muslin was used to designate a woman regarded as an object of sexual desire.

—Cf. the similar use of the nouns crumpet and crackling.

The earliest occurrences that I have found of muslin used to designate women are as follows, in chronological order:
—Note: quotations 1, 2, 3 & 5: as published in Volume 3 of Selections from the Dramatic Works of William T. Moncrieff (London: Hailes Lacy, 1851), by the English playwright William Thomas Moncrieff (William Thomas Thomas – 1794-1857):

1-: From Mr. Tonson; A Farce, in two acts; First performed at the Theatre Royal, Drury Lane, Thursday, September 20^th, 1821 [page 6]—the characters are Jack Ardourly and Tom King:

Ard. What’s the finding an old uncle to the losing an angelic girl?—What’s the favour of fortune to the malice of fate? I’m the most miserable dog in existence.
T. King. Miserable about a wench! muslin-struck quite—ha! ha! ha!

2-: From Tom and Jerry; Or, Life in London; An Operatic Extravaganza, in three acts; First performed at the Adelphi Theatre, Monday, November 26, 1821 [page 4]:

Jerry. (aside to Tom.) I say, Tom—as I hate leave taking, and have a small call to make in the village, let us slip away at once—I’ll meet you there in about ten minutes time.
Tom. Oh! what you’ve got a bit of muslin on the sly, have you—
Jerry. Hush!

3-: From Etymological and Critical Vocabulary and Glossary of Flash and Slang Terms, occurring in the course of this Work, appended to Tom and Jerry; Or, Life in London; An Operatic Extravaganza, in three acts; First performed at the Adelphi Theatre, Monday, November 26, 1821 [page 130]:

Bit of muslin.—A sweetheart.

4-: From Vocabulary of Flash and Cant, as it occurs in Tom and Jerry, published in Tom and Jerry; Or, Life in London: A Musical Extravaganza, in three acts. To which is prefixed a Vocabulary of Flash and Cant, incidental to the Piece. Founded on Pierce Egan’s popular work of Life in London [page 3]—itself appended to Life in London; Or, The Day and Night Scenes of Jerry Hawthorn, Esq. and his elegant Friend Corinthian Tom, accompanied by Bob Logic, the Oxonian, in their Rambles and Sprees through the Metropolis (London: Sherwood, Neely, and Jones, 1821), by the British journalist and author Pierce Egan (1772-1849):

A Bit of Muslin—A Sweetheart.

5-: From The Secret; Or, Natural Magic. A Comic Mystery in one act, first performed at the Adelphi, Monday, Feb. 29 [sic], 1823 [page 15]—the character is Barnaby, servant to Mr. Dearlove:

Bar. (looking out.) Heyday! what can this young lady want, that’s coming up stairs? Oh! I smell a rat—this must be master’s sly bit of muslin.

6-: From The Edinburgh Dramatic Review (Edinburgh, Midlothian, Scotland) of Saturday 1^st March 1823 [Vol. 3, No. 116, page 63]:

Caledonian Theatre.
This Evening will be performed, an Extravaganza, called
TOM AND JERRY
IN EDINBURGH;
OR,
LIFE IN AULD REEKIE.
Tom, (a well known Corinthian, just arrived from London,) Mr. Angus.
Jerry Hawthorn, (more of the Composite than the Corinthian—come to the North by the way of a Finisher, and very nearly bit for his temerity,) Mr. H. Johnston.
Logic, (a chopping Boy, “full of wise saws and modern instances,” tampers with an innocent bit of muslin, and pops into a noose, even “with Spectacles on’s nose”) Mr. Stanley.

7-: From The Road, by ‘Nimrod’, published in The Sporting Magazine, or Monthly Calendar of the Transactions of the Turf, the Chase, and every other Diversion, interesting to the Man of Pleasure, Enterprise & Spirit (London, England) of July 1827 [Vol. 20 (New Series), No. 118, page 166, column 1]:

The Lingo of the Road is amusing. An empty coach is called the mad woman; asking the passengers for money, kicking them; a passenger not on the bill, a shoulder-stick, a bit of fish, or a short one; a passenger who pays shabbily, a scaly one; not paying at all, tipping the double; a glass of neat spirits, a flash of lightning, a drop of short, or don’t stop to mix it; great coats, benjamins, or upper benjamins; putting on great coats and shawls, dressing; a white hat, a lilly shallow; good clothes, a good bit of broad cloth, or neatish toggery; a well-dressed woman, a pretty bit of muslin; a kicker, a miller; [&c.].

8-: From an account of a court case, published in Saunders’s News-Letter, and Daily Advertiser (Dublin, County Dublin, Ireland) of Wednesday 2^nd January 1828 [No. 22,588, page 2, column 3]:

Your Vorship, said Hoskins, I vas on my road ’ome last night, ven I vere coaxed into the holy-land, off Grafton-street, your Vorship, don’t frequent that ere house I suppose, and so much the better for you, as you might be forced to go to a fancy ball, as I vas.
The Magistrate requested him to shorten his story and come to the point.
Hoskins—Is easy coming to the pint your Vorship, I took a rummer or two of grog with a bit of muslin that I saw in the holy land, and ve both vent to the ball in Drury lane.