With a POD of 1796-1805, here's a possible TL for Napoleon's invasion of Britain:
March 1796
Napoleon wins battles in Italy. The First Coalition soundly defeated.
April 1796
The Second Coalition lures the French Army into an ambush and defeats it.
1797 The Year of Mutiny
Plagued by mutinies, including at the Nore, the Royal Navy loses both the
Battle of Cape St. Vincent, (February 14, 1797), and Camperdown, (October
1797).
1798
Britain's woes continue. Nelson loses sight of Napoleon's flagship, L'Orient,
and pursues him to Egypt. The French discover the Rosetta Stone, which is
the key to deciphering the Ancient Egyptian hieroglyphics. Nelson loses the Battle of Aboukir Bay.
1799
On land and at sea, Britain continues to lose. The doddering, mad King George III, who's ruled Britain since before the American Revolution, is forced to abdicate in favor of the Prince Regent, who's immediately crowned George IV. However, even George IV can't stop Britain's reversals, and changes the Admiralty Board, in an attempt to shake up the
Royal Navy.
1800
The Royal Navy's woes continue as it's beset by more mutinies.
1801 Copenhagen
A coalition of small states, organized by Napoleon, defeats the Royal Navy at Copenhagen.
1802
The year opens with good news. The Royal Navy has temporarily rid itself of its troublemakers, and destroys the French fleet.
1803
One year does not a turnaround make. The Royal Navy suffers a new round of mutinies. The Royal Navy goes into battle against the French and
loses big. Half the Royal Navy's ships are captured by the French.
1804 Tripoli
HMS Amazon, one of Nelson's ships that wasn't captured by the French,
is dispatched to Sicily, where Commodore Preble of the United States Navy, is repairing his ships. Amazon's captain informs him that the USS
Philadelphia, the USS Constitution's sister ship, has been captured by the
Tripolitans. Preble sends Stephen Decatur, and a handful of men on the recently captured USS Intrepid, to destroy the Philadelphia. Upon hearing the news, Nelson calls it "The most bold and daring act of the age." The
Royal Navy still loses to the French.
1805 Disaster at Trafalgar
The morning of October 25, 1805, dawned bright and sunny. The Royal Navy, its morale still at a low ebb, after eight years of mutinies, has lost its fight. The only man holding its ragged ends together, Admiral Nelson,
is shot and killed by a French sniper. French Troupes de Marine storm the
British flagship, HMS Victory, and capture it. A prize crew from the French
ship Isle de France, is sent over and brings HMS Victory back to France as
the French ship Victoire.
1805 France invades Britain
The French Navy, led by Napoleon's new flagship, La Victoire, easily pushes aside the Channel Fleet, and manages to land on the south coast
of England. Napoleon then goes to London. King George IV, and the rest of
the House of Hanover, have fled to British North America, to continue the
struggle. Napoleon's the first ruler of France since William, Duke of Normandy, later known as William the Conqueror, to seize the British throne. He sets his brother, Jerome, up as the King of Britain.