The land between Tooley Street and the Thames has been occupied by wharves and warehouses since the middle ages. Hay's Wharf originated as a Tooley Street brew-house of which Alexander Hay took ownership in 1651. In 1656 Hay let part of the wharf and buildings to the New River Company. This became known as Pipe Borers’ Wharf and here trees were hollowed out to make London’s first water mains. The Hay's Wharf Company grew to own most of the complex between London and Tower Bridges.
The current Hay's Wharf Buildings were constructed in 1856 by Sir William Cubitt on the site of the 18th century wharf. Hay's Wharf was one of the earliest complexes to incorporate fireproofing, using incombustible floors of brick arches on cast iron beams. Despite this Hay's Wharf was destroyed in the great fire of Tooley Street of 1861, and then largely rebuilt. The wharf handled all cargoes except tobacco, but specialised in provisions and tea. In the 1860's the use of cold storage was pioneered here and the area became known as "London's Larder". 75% of the bacon, butter, cheese and canned meat needed for London was stored here. In the 1960s the cargo business was revolutionised by the introduction of container ships and it all moved away from the centre of London. Incidentally, don't believe anyone who says the word "wharf" is an acronym for "warehouse at river front". Complete rubbish; the word has an eminently respectable etymology from Old English.
2021: A London Inheritance has an excellent post on Hay's Wharf and nearby.