I'm sure we have a connection somewhere via the Harrison's from Much/Little Hoole and Longton but I cannot yet work it out.
My 5 x great grand parents Cuthbert Harrison (1742) originally came from Freckleton, Lancashire just across the River Ribble from Hoole, in those day's people farmed both sides of the river and travelled across the ford frequently.
My 4 x great grand father Richard Harrison (1780) was a farmer on Turnpike Rd, Hoole and all his children were born in Hoole. He would have been a neighbour to your relative Robert Harrison (abt 1781) in 1851 both are listed on Turnpike Rd.
I need to revisit BMD records for both sides of the river to see if we have any link
If you would like a GEDCOM file of my Harrison data please let me know your email address
Mark