Green’s Dictionary of Slang

1. a tight skirt, fashionable c.1881.

1882		Kerry Eve. Post 29 Mar. 2/1: We do not regard jerseys and eel-skin skirts with any favour.
1891		Blackburn Standard 7 Mar. 6/5: [A]n alarm has been given lately that we stand in danger of sliding back into the hideous pull-back or eel-skin skirts.
1900		Globe (London) 15 Feb. 6/4: Society has not yet recovered its normal gait since the very tight dresses last summer. In one of those eel-skin skirts it was quite impossible for most people to walk with any degree of grace.
1907		Sheffield Eve. Teleg. 6 Dec. 7/2: THE EEL-SKIN SKIRT. Wc are arriving by leaps and bounds at the eelskin dress [...] Skirts [...] are getting tighter and tighter over the hips and across the front.
1917		Sketch (London) 7 Feb. 30/2: No one can want short, eel-skin skirts, and they would not be economical if they have not width, they must have length.

2. tight trousers.

1898

Eve. Teleg. (Dundee) 10 June 4/7: They have been wearing trousers [...] as tight as eel-skins.