Short answers, pulled from the story.
The facility began operations in 1802 after the Navy Board authorized a new system to manufacture pulley blocks using machinery. Marc Isambard Brunel proposed his block-making patent to the Admiralty in August 1802 and established a workshop in the yard that same month.
Marc Isambard Brunel designed the original mechanical systems while Henry Maudslay manufactured the actual machines based on those designs. James Sadler installed a house-built table engine in 1798 to power dockyard pumps before Fenton, Murray and Wood replaced it with a more powerful unit in 1807.
Ten men operated the machinery to meet the massive demand of the fleet despite the ability for a single worker to produce as many blocks as one hundred ten skilled craftsmen. The layout allowed work to progress naturally from one stage to the next without interruption during production cycles.
Production using these original machines finally ceased in the 1960s after over a century of service. Some transmission drives and engine-house shells remain inside the buildings today despite poor repair conditions.
The British Royal Navy faced a desperate shortage of pulley blocks during the Napoleonic Wars and needed over one hundred thousand blocks annually to keep its fleet operational against Revolutionary France. Existing contractors produced inconsistent quality and charged high prices for their hand-made goods so Brigadier-General Sir Samuel Bentham arrived at Portsmouth Dockyard with a mandate to modernize production processes.