Here is one more reference that pretty much seals the location, in my mind anyways.
Bankside/British History
No. 79 (Falcon Drawing Dock)
The Falcon Drawing Dock and the premises on the east side, No. 79 Bankside, are on the site of part of the Falcon Inn. They were leased to Messrs. Newton & Sons, firebrick merchants, the present owners, in 1833–4 by Messrs. Handasyde & Prickett, who had a lease from the Bishop of Winchester. No. 79, the office, was rebuilt in 1840 though it retains two patches of early 18th-century walling. The door and windows facing the dock on what now forms the main front, and those at the north end, are treated with classical mouldings. They date from the rebuilding.
Bankside/British History
No. 79 (Falcon Drawing Dock)
The Falcon Drawing Dock and the premises on the east side, No. 79 Bankside, are on the site of part of the Falcon Inn. They were leased to Messrs. Newton & Sons, firebrick merchants, the present owners, in 1833–4 by Messrs. Handasyde & Prickett, who had a lease from the Bishop of Winchester. No. 79, the office, was rebuilt in 1840 though it retains two patches of early 18th-century walling. The door and windows facing the dock on what now forms the main front, and those at the north end, are treated with classical mouldings. They date from the rebuilding.
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