Normally the GRO reference isn't valid for local office, however in the case of Birmingham they will do a search using the reference, I have found them very helpful

, don't know of any others that will do this.
Have a look at the link on my previous post good explanation about certificates.
Marriage certificates from the local offices are a slightly different matter because of the number of church registers that would need to be searched.
Some councils are putting indexes online which give reference to obtain certificates from local offices, see
http://www.ukbmd.org.uk/Keziah