The arrival of part of Admiral Duncan’s Yarmouth based fleet at The Nore gave a new boost the morale of the mutineers which had been battered by the change of attitude of the people of Sheerness towards them and the defection of several ships to the government, (that story is detailed here).
While their morale may have improved their situation had not. They were cut off from shore, denied supplies, and the government refused to enter into further negotiations with them. Some unnamed genius came up with the idea that two could play at that game and conceived the idea of a blockade of the Thames and, therefore, of London. Accordingly, on the evening of May 31, Richard Parker presented himself at the home of the port commissioner at Sheerness and announced that London was under blockade.
At first, it seemed like this was mere bluster but on June 2 HMS Swan, sloop, began intercepting inbound merchantmen and detaining them. The traffic soon outpaced the capabilities of a single ship and HMS Brilliant (28), HMS Standard (64), and HMS Inspector (16) were called upon to lend a helping hand.
Parker and the mutineers desperately needed a bring the mutiny to an end and this move seems calculated to do just that.