It might be over the county border into North Yorkshire but Sherburn is part of the wider Leeds borough and is probably closer to Leeds than York - it makes more sense it having an LS post code than a YO one.
My mate. bless him says he lives in Sheffield. Aston. but pays his rates to Rotherham. Goes bonkers when I insist he lives in Rotherham. (I may be wrong but who cares) Edit-: Just Googled it. Seems to add more weight to my argument.