Hi Lewis - I've looked at the 1881 and you are right, the neighbour's surname (Henderson) is the same surname as my girl, Elizabeth Henderson. However I think this is coincidence as I don't think there are any Redcar connections with my Hendersons, which is where this chap says he was born. Of course I can't be 100% certain, and something might crop up which changes my mind.
I also checked the Garthwaites in previous censuses, and found that in 1861, George Garthwaite and his family are living just a few doors away from Elizabeth who is listed under her step father's name of Campbell, in Lower Feversham Street, Middlesbrough.
More digging required, but perhaps they were just family friends after all, and not related. I just can't get that Garthwaite marriage witness out of my head and wonder if the two families are linked more formally in some way.
I'll keep on digging!