Backhouse’s Bank was founded in 1774 in Darlington by Quaker, James Backhouse. This ‘branch’ is at Preston Hall Museum. Jonathan Backhouse was heavily involved in the £125,000 financing of the Stockton & Darlington Railway.
In 1896 Backhouse merged with other Quaker banks, Gurney of Norwich and Barclays of London to form what is still known today as Barclays Bank.
I’m not sure which branch this plaque originated from, possibly Stockton given the date and current location ?