What we object to, ALL we object to, is the ‘we saved you’ drivel. THAT’S when we tend to play the 1941 card as a retort.
We did save you. Without Lend Lease, you'd be speaking German today. Without direct American intervention, hundreds of thousands of additional Brits would have died in that war, either in defeat or in retaking North Africa and continental Europe. And that's just WWII. Without American intervention in WWI, hundreds of thousands of additional British servicemen would have died and the war might have ended in a defeat rather than a victory. The only occasions on which British troops have fought in proximity with American troops in which American sovereignty was in jeopardy were during the War of Independence and the War of 1812.
While I'm sure our cousins across the water would jump in on our side if we were invaded, it ain't happened, yet. Until that happens, and Britain sustains large casualties in doing so you kind of owe us, whether you want to acknowledge it or not.