I see that the 1901 census gives Elizabeth's age as 37 therefore a birth year of 1864. So that illegitimate birth I found for Elizabeth may well be correct.
I think you must be correct. If so,
FamilySearch has a baptism at Morpeth 10 Feb 1864 Elizabeth Ann ENGLISH daughter of Ann.
I am a little concerned that North Sunderland was in the Belford registration district. However, the earliest ENGLISH registration in Belford RD was in 1883, and although there were several Elizabeths registered in Belford none of them had surnames remotely resembling ENGLISH.