I'm not 100% on where the stereotype comes from, but I just American-Googled "english bad teeth" and got about 30,900,000 results in 0.40 seconds. I've actually got very good teeth, and have never had a filling or any of that painful nonsense. But superficially (aka in the only way that matters) my teeth weren't exactly up to the exacting standards of America.
I have always been of the mindset that at-home whitening doesn't work, and therefore have never tried it. However, after seeing an article on Into the Gloss, I decided it was worth my time and money - $5 all inclusive. I know what you're thinking, so stop. This is allowed by dentists and isn't properly dangerous - you just need to buy the 3% hydrogen peroxide, which will say something like "suitable for gargling" on it. And for God's sake, don't swallow.
What I do is every evening before brushing, take a small mouthful and swill it about. It has a very specific taste, like chewing on the cuffs of your old school jumper. It will also begin to foam up, which is it dissolving all your problems (aka stains). Then I spit it (don't swallow) and do a regular brush. Because I don't do things by halves, I also bought a fluoride+peroxide toothpaste, which seems to work very well, and tastes like regular mint.
And look at these goddamn results! Look at the glare of the sun reflecting off the snow outside, which in turn is reflecting off my tegs. I didn't take before adn after photos because I honestly didn't predict a big difference, but trust me, this is the whitest my teeth have been in a long time. I'm still drinking all my favourite brown drinks (tea, coffee and diet coke) on the reg, too. It really, really, really makes a difference, doesn't cost a bunch of money, and aside from the strange taste, seems to be without side affect. If you want to follow the "American" tooth trend, give this a go.