There was little welfare available before the 20th century, so people had to find work and that might have entailed moving.
Agricultural workers were usually hired at a hiring fair for 6 months, re-hiring by the same farmer could not be relied upon.
Workers might hear that a different farmer was a better employer or they might discover that the parish they lived in was an ungenerous provider of welfare so it made sense to move, if they could.
If you have ancestors in Berwick or North Northumberland, they may well have lived or worked in Scotland, too, most probably in the Scottish Borders, with Berwickshire and Roxburghshire being the most likely counties.
Borders Family History Society have a special offer on most of the 1841, 1851, 1861 Census Transcription booklets they sell but extremely limited stocks at the special offer reduced prices.
More details on their Publications Sales List.
Northumberland & Durham Family History Society are also advertising special offers on Northumberland and County Durham Census Indexes.