A few hundred miles off the western coast of the Philippines, the roar of American warplanes punctuates the air. The USS Ronald Reagan is carrying out drills above the South China Sea, a 1.4 million-square-mile expanse of deep blue at the heart of a slow-brewing dispute between the US and China.

The action does not go unnoticed. Soon after entering these waters, satellite images show the ship is surrounded by Chinese vessels. The defence ministry in Beijing lodges a complaint, accusing the US of provocation by “flexing its muscles” in Chinese territory.

This bustling, floating city – the size of almost four Big Bens laid end-to-end, the ship carries nearly 5,000 personnel including 5 dentists and 3 chaplains – is here to show strength.

China has long claimed sovereignty over the strategically important South China Sea, in the face of UN conventions covering international waters and competing claims from at least six other countries.

The US conducts regular exercises in the region, joined on occasion by the UK, to assert the right to freedom of navigation in the sea, a growing concern for the $3.4 trillion of global trade that passes through every year.

“There is certainly a disagreement in where they think we should sail,” Rear Admiral Karl Thomas tells The Telegraph on a rare visit on board the ship.