The British continued to wield considerable influence on world affairs, as they do today. But after D-Day, on the battlefields of Europe and in international conference rooms, instead of setting the agenda, the British found themselves having to go along with it.

Ehhh. D-Day wasn't a sudden switch. America's industrial prowess wasn't a secret; in 1940 we were making 6,000 planes a year, by 1942 that had grown to 22,000/year and was at 96,000/year in 1944. In terms of ships, with the advent of the Essex class fleet aircraft carrier the US would go on to launch

1942 - 3
1943 - 5
1944 - 9

...fleet carriers, and in terms of Battleships
1940 - 2
1941 - 3
1942 - 3
1943 - 1
1944 - 1

...along with countless other cruisers, destroyers, escort carriers, transports and many more. By contrast, the Royal Navy launched

Aircraft carriers
1940 - 2
1941 - 4
1942 - 0
1943 - 1
1944 - 2

and battleships
1940 - 1
1941 - 1
1942 - 2
1943 - 0
1944 - 1

...not only that, but Lend-Lease was providing food and other equipment to the UK on an hourly basis. The appointment of Dwight D. Eisenhower as the Supreme Commander of the Allied Expeditionary Force in 1943 further solidified America's hold on the senior partnership.

If that's not enough evidence, the presence of literally millions of US soldiers in Britain starting in mid-to-late 1942 completely taking the threat of invasion off the table also serves.