Len, this sounds promising. Alice was buried in a plot in Allerton Cemetary in Liverpool, and the records show three other interments in the plot between 1912 and 1963. Two of them are family members easily accounted for, but the third, from later in 1912 (from memory, I've not got my notes right to hand) is of a William Myles, who died aged 70.
The most likely explanation seems to be that he was Alice's father, but I'm aware that there can be a long way between 'likely explanation' and the facts!
The story of Sam has been niggling me for a while. He was one of eight children born to William Cockram, a Leicesterhire coachbuilder, but legend has it that he was something of a black sheep of the family who cut off contact with his brothers and sisters after a series of blazing rows. All the other seven Cockrams are well-documented, but Sam has been difficult to pin down.
Thanks for your help,

William