For tracing purposes - 1871 shows specific birthplaces as follows:
Jane = Liverpool
Eleanor = Norwich
John = Lowestoft
Anne = Lowestoft
1851 has Randolph b Lower Wick - extract from IGI Pilot site
Name: Randolph Holroyd Age: 2 Birthplace: Lower Wick, Staffordshire
I'm not sure - but is Lower Wick in Worcs?