The Bowes Museum was built in a grand French style within landscaped gardens, as a public art gallery for John Bowes and his wife Joséphine Chevalier, Countess of Montalbo, who both died before it opened in 1892.
On this site www.barnardcastlelife.co.uk it's called the Market Cross. Very interesting images and text. I thoroughly enjoyed looking around. Cheers, Dave