So, according to That document, Ms. E. Rigby was a hospital worker in 1911. The gravestone of Eleanor Rigby states that she was born in 1895 and died in 1939.
An 1895 birth would suggest that it is the Eleanor Rigby born at Runcorn in the Spring of 1895 who would seem to fit the bill for this grave. There's a bit of travelling involved to get her from Runcorn to the Liverpool hospital for 1911, though. But then again, maybe the 'E' isn't actually an 'Eleanor'...?