Even when the Americans do pronounce ate short, they typically use a different monophthong than the British. The British typically use epsilon; the Americans e, in which the tongue is a bit closer to the hard palate and more tense, creating greater vocal tract constriction. As John Algeo states in British or American English? A Handbook of Word and Grammar Patterns:
eat/ate/eaten : The British preterit is typically /εt/, the American /et/. In American, /εt/ is nonstandard.
The LPD says that/et/ ( the dress vowel) is preferred by 55% of native speakers, /eɪt/ (the face vowel) by 45%. The trend is definitely towards the latter vowel. Only some 28% of older speakers use it, but some 65 % of younger ones do. LPD notes, "In AmE [...] /et/ is considered substandard".
The EPD simply lists /et/ before /eɪt/, indicating that the former is more widely used, for BrE. It gives only /et/ for AmE.
I only ever pronounce "ate" as "eight" and, as far as I am concerned, that is the correct pronunciation. However, pronouncing it as "ett" is very common in the UK.
"I ate it yesterday" can sound like "I ett it yesterday".
Some people also mistakenly use it instead of "eaten". Instead of saying "How many have you eaten?" or "How many did you eat?", you might hear "How many have you ett?"
Without wishing to sound like a snob, I associate this pronunciation with lower-class or less-educated people. That only goes for my own region of the UK. I have no idea if it's an acceptable pronunciation somewhere else in the UK.
I recall that when I was a very young schoolboy my teacher denounced "et" as incorrect, just as he did "ain't". And in the 60 or so years since then, I have never once heard anybody say "et." That's how rare it is in AmE.
For clarification, "ett" is the pronunciation I associate with lower-class/less educated/common people.
Here they are:
ate - Definition and pronunciation | Oxford Advanced Learners Dictionary at OxfordLearnersDictionaries.com
ate verb - definition in British English Dictionary & Thesaurus - Cambridge Dictionary Online
They say /et/ is the standard pronunciation in the UK.
Well, two of the leading pronunciation dictionaries, LPD and EPD, give the pet/bet pronunciation as the more common in BrE. In the LPD, Wells says that 55% of speakers of BrE use this pronunciation, while 45% prefer eight. It's interesting to note that his graphs shows only about 28% of older users preferring eight, but 68% of younger users. He says that in AmE, the pet version is considered to be substandard.