It’s pretty simple actually.
In most of our minds, we overthrew our English overlords with the oppressive monarch, the King of England, back in the 1700s. Kicked his troops quite literally back into their boats in the sea.
Fast forward 250 years, with many of us not being given a solid history of the UK itself, and ya’ll in the UK having a common government, we just view you as one “unit”. Sort of like how most of the world thinks the USA is New York City or Los Angeles. That’s not the case of course, but that is how many view us.
And since our primary fixation on the UK is England, the UK = England in a general sense from our perspective.
Obviously not true, but neither is the assumption about the USA either.
Also, to clarify, being from Texas, I don’t own a horse, cowboy boots, a cowboy hat, not a lasso. I do have a gun however, so that part of the stereotype does hold true for many of us.