Hi
To search under both surnames for a 10 year period would involve downloading 80 GRO images and searching for the info - quite a daunting task for anybody. If May was only her middle name and is only shown as an initial - not in full - then every Potter entry would have to be searched to see if it could be matched to a possible maiden name of Bendelow
As far as I know her mothers maiden name is Bendelow
The full GRO index is available to search yourself at your nearest main library and you may find that your library also has free Ancestry access.
I would strongly advise that you try and obtain more positive information before searching
The index can also be searched online if you have an Ancestry subscription or at
www.findmypast.com which is a paysite