Green’s Dictionary of Slang

the hobbling walk affected by invalids taking the waters.

1881		Derby Dly Teleg. 27 Sept. 4/2: Thanks to a recent sprain, [...] I had the ‘Buxton limp’ to perfection.
1883		Daily News 31 Aug. in Ware (1909) 58/2: If walking is too severe exaction just at first and the ‘Buxton limp’ is too decided, the patient secures a seat in the omnibus.
1890		Manchester Courier 22 Aug. 3/5: To have the ‘Buxton limp’ not merely argues the possession of gout in both feet, but of gout so excruciatingly painful that [etc.].
1909		J. Ware Passing Eng. of the Victorian Era.