Now I can't stop looking

Are you sure about the first child? There are the following on FreeBDM with mother's maiden name Smith
Births Sep 1914 Righton Elsie M Smith Warwick 6d 1756
Births Mar 1916 Righton Walter L Smith Warwick 6d 1442
Births Jun 1918 Righton Eric Smith Warwick 6d 1376
Births Sep 1920 Righton Alec Smith Warwick 6d 1738
Births Mar 1922 Righton Hickford W Smith Warwick 6d 1587
Births Jun 1925 Righton Doreen M Smith Warwick 6d 1418
They could, of course be a different family - if they are yours, the names might be a clue to Alice - especially Hickford - looks rather like someone's maiden name
Trish