If you wanted to get the cert, you would need to order with the name as 'female' but then without the specifics of the GRO reference - vol & page. In that way you would then get the opportunity to add in the names of the parents and a date of birth.
Doing this type of search is speculative in that if the name of either parent in the birth entry doesn't match, then you won't get the cert .
The GRO do not offer partial refunds anymore.
You only get the full refund if they can't supply because the info doesn't match.
The local register office may be willing to help if they have the time. Many do not. But they can be more flexible in their approach if you actually get to speak with someone.
I think their call centre number is here, it appears on other parts of the registration website.
http://www.cambridgeshire.gov.uk/info/20105/deaths/18/registering_a_deathor here
http://www.ukbmd.org.uk/genuki/reg/regoff.html#339CBut you might have more luck sending an email.
Be prepared though for a basic yes or no answer to your question. The reg office is not obliged to give any further details unless you pay.
Please DO NOT contact the BMD-certificates link that Ladyhawk posted. They are just unofficial middlemen and will charge you £25 for a cert.
