I am assuming for Ada to be so far away from home, Barnet, at such a young age, her parents may have died. Although looking at the 1911 index, an Ada Allen in resident in Barnet of the correct age, so it looks as if she had returned. Which to me means close enough family remaining to give her a reason to go back.
However, her father, is not noted as deceased on her marriage of 1918, so perhaps it was just her mother who died and her father couldn't cope.
Any deaths for a William Alfred Allen or Anna Maria Allen in the Barnet area?
Regards
KA