Annie, it wouldn't be unreasonable for somebody living in Widnes to have been born in Bickerstaffe, they are close enough to each other for it to be feasible.
Go to
www.maps.google.co.uk and enter Widnes. You'll see a green road Watkinson Way heading north, follow this north, cross the blue motorway M62, the name becomes the St Helens Linkway, when it splits take the fork to the west, it crosses East Lancs Road and becomes Rainford Road and the Rainford Bypass and then just before you reach the next motorway M58 you'll see Bickerstaffe on the west. So you see there was likely a direct-ish road through from one place to the other via St Helens, no great distance really.
Do you have their occupations? Bickerstaffe is pretty much open farmland, there's a pretty windmill there too, and maybe they just moved to find better work.
Peter would have gone through Bickerstaffe to get to Ormskirk for your book!!!
Your rellies are getting closer to mine hon, we might meet sometime

Mary