My Grandmother was a Horrocks who traced her ancestry back to the Horrocks's of Penwortham near Preston. At the moment I can't locate what genealogical infomation I have on them, but will post another reply when I do, I warn you not to be too hopeful because the information may well have disappeared in one of my many moves.
You may be looking in the wrong town, I do not know where Bolton-Le-Moors is, but what references I do have only mention Penwortham.
My 4th or 5th x Great Grandfather was John Horrocks, a manuafacturer of cotton cloth and also MP for the Borough of Preston, sorry no dates. His eldest son was Peter Horrocks whose first male child: John Ainsworth Horrocks was born in the family home on March 22, 1818. This would tend to confirm that we are possibly talking about the same family. One thing though if Alice is related to John Horrocks then given the dates I would think the mostly relationship would be that they were either siblings or cousins.
In any case this should give you something to look at. The fact that John Horrocks was an MP should mean there are records in the British Parliament.