All true! Family Search has entries for a baptism and a burial for Alice on the same day, but there is an Alice with a mother Susannah in later census so it's possible the next baby girl was Alice - that ones birth is appropriate. And an Alice was a witness at a wedding, as pointed out.
Shippen is in Berkshire and I can't find a baptism for James there. Nor can I find a marriage for John and Susannah, when/if I do all may make sense.
Another reason for dithering about Alice was that mum Susannahs' place of birth varied from census to census. In 1871 it was somewhere in Middlesex but I discovered there is also place in Wiltshire, more likely, but how did Middlesex creep in?
Anyway, thanks for your thoughts and suggestions
