Even on D-Day in 1944 British and Empire forces outnumbered US troops. It was only after the French ports had been opened, the bridgehead established, that the US became the senior partner. Then, the products of America's massive industrial economy flowed across the Atlantic in Liberty ships, themselves often built in just a few days, and the US' vast manpower soon dwarfed our own armies in Europe.
Cameron's comment was a howler of epic proportions. So I'd suggest some Summer reading to sort those difficult dates out; first, the best of the readable correspondents - Alan Moorehead's classic trilogy on the Desert War 1940 - 1943 takes us from the end of the beginning to the beginning of the end, and 'Eclipse' remains one of the best accounts written of the end itself. William L Shirer, one of Ed Murrow's 'boys', broadcasting regularly from Berlin through 1940 and only leaving in December of that year, gives us 'Berlin Diary'. Ernie Pyle's quartet of books, though only started in 1942, is a useful addition.
Then the 'heavies' - Ian Kershaw, of course, but not forgetting Alan Bullock's early work nor Trevor-Roper's account of the end, to give perspective to exactly what we faced alone in 1940.
Readers may suggest several others, but the above should be a decent enough selection for the obligatory week in Rock and later in Tuscany for longer.