So to clarify, you are descended from William Taylor's second marriage but you are looking to find the name of his first wife?
If this is correct then there is a way forward. William's second marriage certificate will have his father's name (or you may already know this). You can apply to the GRO for a certificate where the father's name matches. In the certificate ordering system, check "no" when asked if you have the GRO reference then follow the instructions. They will search a three year period for you and only supply a certificate if they find a match based on the criteria you specify. If they find a match the fee is the standard one (£9.25). If no match is found this is refunded. Doing it this way takes a bit longer (up to 15 days rather than the usual 4)