This has been a difficult site to pin-point with any precision...so this choice of location is an "educated-guess", but I think it's pretty accurate. Dockray (Dockwray) Hall was the site of a fortified tower with an attached chapel dedicated to St Anne. The tower and the chapel appear on most old maps, up until around 1938...the most recent map I could find with any mention of the buildings. Even then, the tower and the chapel were no more, and the site is labelled as "Dockray Hall Barn , on the site of Dockray Hall". It would appear that elements of either the chapel or the tower, or both structures were incorporated into a barn (a house in some records) that was still extant in the 19th century. The chapel was still standing in the 16th century when Machel was travelling the area cataloguing the fortifications of the region. It would appear that the tower and the chapel had an encircling wall. Whether this would have constituted a curtain wall or a simpler barmkyn, is not known....but on John Speed's map of Kendal, dated 1610, Dockray Hall can be seen at the top left hand corner within a square compound, possibly a wall.
The site, shown above, is at the modern day junction of Burneside Road and Elm Court. This area is raised above land to the East, and lays about 400 yards to the West of the River Kent. Originally, as shown on maps up to 1938, the area was open fields. A map dated 1898, shows hardly any buildings to the North with the buildings of Union and Cross Street the nearest structures to the South. These days, there are houses to the North, South, East and West....with just a small section of wooded area showing where the tower and chapel may once have stood.
There is a connection between Dockray Hall in Kendal, and Borwick Hall near Lancaster....both fortified residences, and both the homes of wealthy local land owners. Borwick Hall was the home of Sir Robert Bindloss (died 1629). Sir Robert married Alice, daughter of one Lancelot Dockray, owner of Dockray Hall.
There is also mention in local historical documentation, of the Phillipson family, who also held Hesfell Hall in Kendal, and Hollin Hall near Crook. The family were staunchly Royalist, and it's therefore likely that, at the same time they lost Helsfell Hall to the Parliamentarian authorities, Dockray Hall was forfeited by them. It's likely that what was saleable was sold off, and the remains demolished, except the chapel which was then converted to a house. There are now no remains of any of the buildings, including the barn.