I think this might be Eliza in 1911 - she is the only Eliza King coming up as born in 1884/5 in Suffolk anyway:
KING ELIZA (RG14PN5775 RG78PN263 RD93 SD6 ED9 SN235)
Address IVY LODGE THE SQUARE FRESHWATER BAY County Hampshire
District Isle of Wight Subdistrict Calbourne
Enumeration District 9 Parish Freshwater
This is the household:
ANDERSON, EMILY HEAD SINGLE F 50 PRIVATE MEANS LANCASHIRE CHILDWALL
ANDERSON, JANE SISTER SINGLE F 45 PRIVATE MEANS LANCASHIRE CHILDWALL
KING, ELIZA SERVANT SINGLE F 26 COOK SUFFOLK BARTON
ENEVEN, MAY SERVANT SINGLE F 17 HOUSEMAID YORKSHIRE ACCOMBE
Do you think this is her? Does help with the Smith connection though!!! Will keeplooking for you.