Well, you answered the most exciting part of it in your question: the French and Spanish fleets laid siege to Gibraltar from June 1779 until February 1783. It did not end well for them. Relief expeditions from the Royal Navy were consistently able to sail through the Franco-Spanish blockade, and British gunners destroyed the besiegers' floating batteries - rafts with heavy siege artillery - with heated shot. The result was the fiery scene John Singleton Copely painted in celebration: (https://upload.wikimedia.org/wikipedia/commons/4/48/The_Siege_and_Relief_of_Gibraltar_(2).jpg).

But we've started at the end. Let's go back to the begining of open hostilities. At sea, British, French, Spanish, and American shipping did their best to interdict and raid each other. The only major sea battle fought in European waters was off Ushant in 1778, an indecisive engagement where the French did not weaken the British navy to the point where the French army could attempt a landing on the British mainland.

American raiders were not absent from this naval war. John Paul Jones raided off the Irish coast in his French-built Bonhomme Richard, running up a respectable tally against British commerce until he was finally run down by the British frigate Serapis. In the ensuing battle, Jones yelled his famous utterance "I have not yet begun to fight" and captured the Serapis even as the Richard sank from under him.

Britain never made any attempt at invading France itself; between North America, the Caribbean, India, and its own defense, they simply did not have the manpower to mount an offensive. The manpower squeeze on the army led the Crown to attempt to loosen the restrictions on Catholics serving in the military. Anti-Catholic backlash, whipped up by the eccentric Lord Gordon and his Protestant Association, culminated in five days of destructive rioting in London in 1780 which killed nearly 300 people.

With an invasion of the England proper impractical, the French invaded of Jersey, one of the French-speaking islands in the English Channel, in 1781. Jersey was a British supply and privateer base, and its loss could help reopen the possibility of a larger landing elsewhere. The attack devolved into a street fight, later commemorated in another Copley masterpiece. Once again, the French were repulsed with considerable casualties for the size of the force.

I think you can see a pattern here: a lot of very threatening maneuvering and raiding created plausible threats to Britain that only in hindsight do we know never actually materialized. The War of American Independence was never hugely popular in England, but threats to the home island and the empire helped collapse political support for the war.

I have some MAJOR reservations about the domestic portions of the book, but Thomas Flexner, The Perils of Peace does a capable job showing the international aspects of the American Revolution.