Irene,
I too am struggling over the issue of RC services performed with or without benefit of a church or chapel ( Cowpen,near Blyth)
Michael Gandy has written several books on the history of Roman Catholicism in Northumberland ( and also the rest of UK )
e.g. "Catholic Missions and Registers, 1700-1800"
For Berrington he writes that there was a "domestic" chapel from late 1700s, sponsored by the Clavering family.
The adjective "domestic" usually meant that the chapel was either in a house, was attached to a house, or adjacent to a house and was usually private ( like Croxdale in Co Durham)
In this case , likely to be the Clavering house in Berrington.
There was a similar situation in Haggerston, with the Haggerston family, which was served by Jesuits up to 1805, then by Bendictines up to 1846.
Then it gets complicated... Berrington and Haggerston were then included in the territory served by the parish priest from Wooler, St Ninian, saying Mass about once a month throughout his area. This also included a mission at Ellingham and services at Seahouses.
This continual changing of arrangements seem to show the RC church , in early days, struggling to provide an efficient and practicable services to area prior to the re-establishment of the church in England.
But I do not know whether the Berrington "domestic chapel" is still standing. Maybe the 1993 Michael Gandy book, " An Atlas", which shows dating and location of RC churchesand chapels, will provide the answer.
Michael Dixon,
Blyth, Northumberland