This appeared in the pages of The Lady’s Monthly Museum (April, 1822) among other editorial content, suggesting this is a great joke. Leg Alley was a narrow alley in Shoreditch (London). There were also Leg Alleys elsewhere in the UK.
Check it the Shoreditch Leg Alley on the 1677 Map of City of London: https://www.grubstreetproject.net/london/#map=62/categories=195/@73846,5635,12594z
