Cannot at present see any connection between your Kayes and mine, but the Kaye name was so popular in Honley in the 1800s, it's still more than a possibility that there is some distant relationship. My GGF Alfred Kaye and his brother Wright Kaye left Honley for Leeds in the early 1850s. Alfred went first to Holbeck and then later on both of them are living in Burmantofts. The reason for this is because Alfred was a partner in the Hardwick Brothers cloth finishing mills and Wright was an overseer there. The mill was in Mushroom Street, Burmantofts and I have considerable information about the mill from its founding until it closed in 1890 - the cloth they produced went out of fashion. Alfred died at 46 Cowper Grove, Harehills, one of Leeds well-loved but now virtually extinct back-to-back houses, in 1915.
A lot of my Kayes are buried in Beckett Street Cemetery - I have quite a long list of them, including also connected families - Allen, Hardwick, Littlewood, Watson, Hudson, Lawrence and Camidge.
Alfred Kayes parents were George Kay and Ann (almost certainly) Booth. Don't know about George Kay but his wife Ann certainly escaped from Honley to Leeds and was living at 40 Granville Terrace in 1871.Cannot at present get any further back than George Kay and Ann.