If this is the last answer you need then you should be able to help us to help you by giving the first letter!
Already posted my entry with several blanks including this one but with this info might be able to offer an idea
Hard when you are not doing the quiz, but some stately homes beginning with B are:
Badminton House
Belton House
Blenheim Palace
Blickling Hall
Bowood House
Burley House
You would have to google image them and compare them to your picture.