Dictionary of National Biography have an earlier one;
Thomas Butterworth Bayley (1744-1802); born in Manchester, son of Daniel Bayley (Daniel Baylet was trustee of Cross St Unitarian chapel); married Mary Leggatt, daughter of Vincent Leggatt.
Archive.org have a scaned copy of "The Family of Bayley of Manchester and Hope" writted 1894, which might be helpful
http://www.archive.org/details/familyofbayleyof00axon There is a chapter on the Bayleys of Withington which says James Bayley of Withington (1705-1769) had four sons (and ten daughters) The four sons were:
Samuel, had one daughter, Anne
James, died in infancy
John, died unmarried
James, had no children
If that pedigree is correct, it's looking doubtful that your Thomas is a direct descendant of the Withington Bayleys, unless there was an illegitimate line - but the book may have some other lines you could investigate.
Good luck

Barbara