earlier i think i might have mentioned wills, obviously the first place to look would be for Matthews will if he left one did it include family members other than wife and children?
if not it might be worth seeing if there are other wills for Cockcrafts and variants in Yorkshire and seeing if these mention Matthew
first of all you have to identify where the probate may have been granted unless you are aware of his residence approx. year of death and rough idea of wealth this may be difficult.
however you could try origins.net this holds the York Peculiars Probate Index 1383-1883 the originals are held at the Borthwick Institute but you can order copies online.
re the manorial records i mentioned earlier in the early days of the 1700's there were NO major population centres apart from London (in 1800 London was the largest city in Europe) the next largest was Bristol and the third was Norwich.
next came York, Nottingham Exeter Worcester etc. with populations of 10,000 and then the next tier was Manchester 6,000 and Liverpool and Birmingham 4,000 each (thinks to herself wonder where Leicester is on the list)
so England was a rural country until the industrial boom.
the majority of its people lived in villages and hamlets clustered around market towns with the larger ones acting as hubs for the local economy and providing a base for commerce and industry.
York itself is on the River Ouse and would be a fishing centre as well as on the main road through England to Scotland.
anyway i go off on a tangent.
within these rural communities there were 2 main admin. units the parish and the manor.
the parish and manor boundaries may be different, in theory every manor had a 'lord' who would grant strips of land to people within the manor in return for service, so although the farmers farmed land in the manor they would have to give the 'lord' some of their crops or they could just pay the 'lord' for the use of the land. at the end of the lower end of the social scale you had cottagers who worked the 'lord' land but had no land of their own.
thirdly it has been passed down the Matthew came from Flamborough i dont think you would come up with a name of a town like this unless you had some reason to know the town so dont discount it