It's less noticeable in, for instance, southern accents. 'Generic' news-reader mid-west accents a good for this.
It's the cliché that Americans pronounce the T after a vowel in words as a 'd' sound, 'warder' for 'water' etc. Someone up thread commented about 'brits' being careful to enunciate their 't's, which I assume was related to this.
Those sorts of 't' sounds (I forget the name) are problematic in a lot of English dialects, I'm surprised no-one has complained about people down south using the glottal stop when they talk, as they generally occur in the same place. Instead of 'warder' you get 'wa'er'.
The Prof explained the reason but it is interesting to try out, especially in mixed company because you can end up with the British half of the room swearing there is no difference and the Americans getting the right answer every time.