I found 5 different william warburton's in the bmd's (manchester or greater manchester are in 1846) if you know the month that will also cut that down, but from the bmd's I have ordered if you put in reference points of facts you know, they will not send you anything that don't match. they do keep a portion of what they charge on the ones they don't send but not the full shot plus they name birth parents (if supplied) on the certificate of birth.
England & Wales, FreeBMD Birth Index: 1837-1983
about William Warburton
Name: William Warburton
Year of Registration: 1846
Quarter of Registration: Jan-Feb-Mar
DISTRICT: Manchester (1837-1924)
County: Lancashire
Volume: 20
Page: 761 (click to see others on page
William Warburton
Year of Registration: 1846
Quarter of Registration: Jul-Aug-Sep
DISTRICT: Bury
County: Greater Manchester, Lancashire
Volume: 21
Page: 339 (click to see others on page
William Warburton
Year of Registration: 1846
Quarter of Registration: Jul-Aug-Sep
DISTRICT: Chorlton
County: Lancashire
Volume: 20
Page: 316 (click to see others on page
England & Wales, FreeBMD Birth Index: 1837-1983
about William Warburton
Name: William Warburton
Year of Registration: 1846
Quarter of Registration: Jul-Aug-Sep
DISTRICT: Manchester (1837-1924)
County: Lancashire
Volume: 20
Page: 648 (click to see others on page
England & Wales, FreeBMD Birth Index: 1837-1983
about William Warburton
Name: William Warburton
Year of Registration: 1846
Quarter of Registration: Oct-Nov-Dec
DISTRICT: Rochdale
County: Greater Manchester, Lancashire
Volume: 21
Page: 737 (click to see others on page)
hope this might help