HELP!!! with a difficult record

I'm searching for a record and have come up with nothing, I don't know if others could help, I'm trying to find a birth certificate, it might not be possible on the internet, now the record is for my nanna, she was called Nesta Mary Eunice Smith, she was born March 22nd 1931 and died in 2003, and worked in the Elba factory in Swansea, now the difficult part, she was adopted 3 times, her birth surname was Guppy, and I don't know if her forenames were changed after the adoptions.

HELP!!! with a difficult record