Jacksi -- now the General Register office are showing mother's maiden names for births from 1837.
If you haven't used the site before you will need to register - but it's free to search. You can also order certificates from that site if you wish.
https://www.gov.uk/general-register-officeOnce you have registered - simply go to 'Search the GRO indexes.'
It is a bit cumbersome in that you can search a particular year and plus or minus 2 years. You also have to identify the sex.
In your case I actually found the year and registration district on FreeBMD first - so that I knew which District to input - as you cannot search by County on the GRO Index.
Finding a mother's maiden name is SO useful though.
(You can also find ages at death from 1837 -- ie before the year they appear on Free BMD.)
You cannot search for marriages on that site.
I cannot find a marriage for your William Walker at the moment.