With a name as frequently occurring as White, the crem may need more info other than their names, full names and dates of death are a must and then most probably their last known address.
If Southport crem can help, the GRO reference numbers won't be required as they will mean nothing to them. The ref numbers only mean something to the GRO, they don't even tie up at local reg offices with their records.
However, if the crem can't help then post again with the reference numbers as that will indicate an area for the chatters here who may be able to help.
Dawn