Hi Ann,
Thought I'd just give you a tip before you contact the cemetery, in case you haven't done so already.
I contacted New Southgate Cemetery after buying my great great grandfather's death certificate to find out when and where in the cemetery he was buried.
I don't think they could have been MORE helpful towards me - I did have have slightly unusual circumstances though, as my gt gt grandfather was buried there in a common grave as he was being detained in a intern camp during the First World War.
They checked the record books whilst I was on the phone to them. They told me that there was a memorial placed by the German government which his name should be on and asked me if I would like to have somebody go down to the memorial and take a photograph of it and e-mail it to me. I received the photos within the hour.
About a month or two after this (I contacted them around August of this year), me and my family went up to the cemetery to see the memorial for ourselves. The staff there asked if we would like to see the original record books and they took us into a room to see them.
Anyway, I'm not guaranteeing that you will get the same treatment, but I would definitely buy the death certificate with the GRO before contacting them. Then you will have a death date to give them and they will have a lot less work to find your relative. I always find having the exact date of death gets a much more positive response from cemeteries when asking for burial information.
If you just say 'he/she died in this quarter of the year' that can widen the search from around a week after the date of death to sometimes looking through a whole record book full of burials. They're a commercial business and this all takes up time.
I hope you find what you're looking for!