Possible??
SULLIVAN, ALICE TERESA
Mother's Maiden Surname: PADDON
GRO Reference: 1913 J Quarter in KENSINGTON Volume 01A Page 215
Looking on the free index to the 1939 register for Alice's born 24.3.1913
One is
Alice Sullivan, 1913, living 59 Sellons Avenue, Willesden, with James Sullivan, born 1881, and Alice Sullivan, born 1882
Also two other females, who may be other daughters of James and Alice and who may have birth registrations with mmn Paddon.
So, if it might be her, were she and William really married?