Valda,
The birth certificate says the mother is Emily King. I'm afraid I think Emily Lena King is a different person.
I can't find James Russell King's marriage certificate as I don't know who he was married to. The closest match I can find is a James King, married to an Emily Cottrell with a daughter called Emily also who would be about the right age. And the records are all based in the Kensington area of London which would be about right. But i've no way of confirming this.
I had a thought, could Emily have been residing at 62 S.Molton St illegally? ie squatting? I want to identify this woman so I can see when she died and if she married/had more children before she died!!
I live in Somerset, and Uplyme/Lyme Regis is my local beach so I know the area well.