Has this actually happened to you, or is it a hypothetical question?
It won't be an issue, though I'd be surprised if they were using a stamp with the wrong date on it. If it is the case that this has happened though, you could just make a note on the application form to say that you actually arrived on the 19th but for some reason it was stamped the 20th.
Just to check though: it's not the case that you left the US on the 19th, but actually arrived on the 20th? Most US to UK flights are overnight, so you often end up actually arriving a day after you left.