Welcome back!
You are right when you say that there were lodging houses at the entrance to Mugger’s Neuk in 1861. There were in fact two, but in 1851 these were one larger lodging house. As I mentioned earlier, housing was scarce for the increasing workforce so as well as the lodging house which housed 17 lodgers (and the family of three who ran it), there were a further 60 people lodging in the market place within the homes of various families. However, I don’t think your relatives were lodgers of either sort.
In 1851 there were no Dixons living in the lodging house or lodging with private families in the area where the lodging house was ie. the market place. If your relative is who I think he is, Charles Dixon with father of the same name and a mother named Dorothy, then he did live in the Market Place just to the left of the Howard Arms when facing that building. Why do I think this?
The enumerator’s route, 1n 1851, went from “the first house in the corner below the Cross to the last house at the east end of the town on the same side”. He then crossed the road and enumerated “the south side of the town from the first house in the Mill Yard at the east end to the last house in the Half Closes on the same side”.
There was a general lack of postal addresses in the 1851 census as the postal system hadn’t really developed at that time. However, there were schedule numbers for each household in the census documents and certain locations were identifiable by the occupation of the residents – such as “innkeepers” and “grocers” who usually lived on the premises.
Looking at the 1851 census for Bedlington, district 2a (which includes the market place), and following the enumerators route, as he himself describes it above, the first house below the cross has schedule number 1. Successive sch. nrs. are given in sequence to the various households along the route. NB. The sch. nr. applies to a household, NOT a building. There may be several households in one building.
Continuing eastwards in the enumerator’s footsteps from Muggers corner towards Leadgate House (on the corner opposite the Northumberland Arms) you will find at sch. nr 29 an innkeeper with the unusual surname Petrie. Unfortunately, there is no name to the inn. However, if we look up Petrie in the following 1861 census, we can see that he is in the same position and that his business is the Howard Arms. That sorted out we leave sch. Nr 29, the Howard Arms, and get back onto the enumerator’s route.
We don’t have to go far to find Charles and Dorothy Dixon together with 5-year-old Charles Dixon and his siblings because he is at sch. nr 31, almost next door to the tavern. At sch. nrs. 30, 31 and 32 are three small households which probably, but not certainly, occupy the small row of buildings which I’ve arrowed blue in the map below. What I can say with certainty is that Charles Dixon lived in one of the buildings - or the buildings in the yards behind them -which I’ve marked in red.