Hi all thanks for your help,
The Kate Mitchell born in 1911 also dies in 1911 I believe thus ruling her out. I ordered her birth certificate and then was searching deaths when I come across it.
Thanks for the fascinating information about the Bridgewater's it is possible that he wasn't a doctor as this wasn't really confirmed.
I was given permission to access the Dudley Road records at Birimingham Central Library and visited last Thursday,
How ever the records had been through flood and fire damage,
Thankfully I managed to find an entry for Kate Mitchell.
The info was:
Name: Kate Mitchell
Age: 26
Ward: Mty
Admittance: 24/12/1935 (The day she had my nan? :S )
Discharge: 02/01/1936
In the end column there was the word 'hoodville' or possibly 'woodville'. The Column was headed Ledger Folio.
I looked at other people with something in this row and found that they had 'Selly Oak', 'Birmingham Infirmary', 'Oaklands' & 'Yardley South' in I believe maybe hospital transfers???
I am wondering did she have to have a Caesarean and was brought to Dudley Road?
Sadly the book with name and address of next of kin was destroyed

Any thoughts much appreciated,
Rach