What if Napoleon invaded Britain?

I recently found out about Napoleon's plans to dominate the entire world. Between 1803 and 1805, Napoleon amassed a huge amount of troops near Calais, also thanks to the funds raised with the Louisiana Purchase (1803). One of the plans that fascinated me the most was the aerial invasion of Britain. He planned to actually land his soldiers via hot air balloons through the Channel, directly into British soil. While many contemporary generals thought of this idea as absolute madness, I think he could have actually had some chance of success. Balloons had already been used for military purposes during France's revolutionary war (1794) and the only real obstacle for balloons on the Channel was the wind. But let's imagine weather was not an issue. French soldiers were better equipped, more experienced and could have received a specific training for balloon landings. The British Army would have been knocked out after a few months, and by capturing London (the capital) and Portsmouth (the main navy base) the French would have gained absolute control over Britain's fighting capability. What do you think? Was this scenario possible? What would a French-dominated Britain have meant for the years to come?