This is known as the Constable's House. The constable of the castle that is. It is - here -
beneath the +
Here is an extract from a really good article from the - Christchurch Local History Society -
web site :-Circa 1160, a stone-built house, usually known as the Constable's House, was built in the bailey on the bank of the mill stream. The ground floor, lit by four slit windows, was used as a storeroom. On the upper floor, reached by external and internal winding staircases, were the hall and solar. The hall was lit by five recessed two-light windows; those in the north and east walls retain their external ornamental carving, while the taller north window also has decorative carving on the inside, as it was above the high table.
Between the two windows in the east wall can be seen the site of the fireplace, whilst above it is a beautiful cylindrical chimney, one of only five Norman chimneys surviving in England and one of the three oldest in the country. In fact, it is the only one of these three that still has its house attached to it! Documentary evidence suggests that originally the building could have been roofed with Devon slate.
During the first half of the 13th century the sanitary arrangements were improved by the construction of a garderobe tower over the mill stream, the lower part of which can still be seen. Later on, a watergate was cut through the east wall, giving direct access to the stream, where there was probably a wooden wharf. Documentary evidence indicates this occurred around 1260.
On the green, to the far side of the building, is the local Bowls Club.