With the free access week on Ancestry, I was messing around with various family surnames, and, lo and behold, up popped this very family group on a Form 30, Canadian Ocean Arrivals!
Seems Andrew, Margaret and the children, all recorded as
Lillie, headed off in 1924 to Hamilton, Ontario, with intention of settling in Canada. Address going to was that of their 'cousin', a Mr Broadbent of 143 Lottridge Street (googling the address and surname brought reference of an Ernest Broadbent and Mary Wright of said address, as witnesses to a wedding, also in 1924
http://homepages.rootsweb.ancestry.com/~maryc/went1924.htm).
No sign of what became of Andrew and family after 1924 though - so methinks I need to enlist help of the Canadian board.