Hi,
If you can't find the birth certificate for Thomas Swift you could try for Richard's which would give you some more information about mary:
Sep 1857 Swift, Richard, Wolverhampton, 6b, 417 according to FreeBMD
One interesting family in 1851 in New Street Portabello, Willenhall, that may be worth investigating:
Thomas Price, 27,
Mary Price, 26, Shrewsbury, Shropshire
Ann Price, 3, Shrewsbury, Shropshire, England
Thomas Price,7 Mon, Bilston, Staffordshire
Class: HO107; Piece: 2020; Folio: 391; Page: 41
Deryck