Brits and Americans might speak the same language, but you'd be surprised how much the dialects vary when you scratch the surface. I am a UK native, but I lived in the U.S. for nearly seven years. I edit a solid combination of U.S. and UK material, and I am here to tell you, the average Brit cannot write in American English and expect to fool an American audience.
There is the obvious: Americans hate the letter 'u' and love the letter 'z'. Most British authors writing in American English can navigate that particular quirk of the language, but there is a lot more to it than than. Brits tend to use a lot of vocabulary that Americans would never use. For example, 'being made redundant' is a common phrase in the UK, but most Americans would never say this. And that's just one of hundreds of examples. Many authors who have a mixture of American and British characters might have encountered some of these issues. It's even more challenging if you are trying to write the whole book in American English.
Grammar varies somewhat between American and British English too. For example, Americans often tend to opt for the simple past tense where most Brits would use past perfect. Where a Brit might say 'at the weekend', an American would use 'on'. Even writing simple thing like dates and times can stir up some contention. If the book has a more informal tone, it is particularly obvious whether the author is American or British, since there are a lot of subtle differences in language and tone.
Then there's the punctuation. There are a lot of baffling differences, like em dashes and whether commas and full stops (periods) go inside or outside quotation/speech marks. There is also the puzzle of whether to use double or single quotation marks. Since this can be challenging enough as a Brit writing British English, you can imagine the headaches when venturing across the pond.
You can have a solid stab at it, but it's likely that you won't be able to flawlessly carry off an attempt at American English.
This is far from true of every American reader, but many Americans enjoy the vibe of an authentic, unapologetically British book. Sure, they might not understand every word, but they will love the atmosphere that it evokes. This is particularly true if your book is set in the UK. For a lot of readers, it is more jarring to have a book with British characters and a British author in American English. However, there are those American readers who won't pick up a book if it's in British English, as unfamiliar style can be distracting as they read.
Another issue with writing a book set in the UK in American English is that you have to make some tough editorial decisions. Do you have your characters saying 'courgette' but use 'zucchini' outside of speech? It's best to avoid such messy questions altogether. On the other hand, that is a strong argument for venturing into American English if your book is set in America.
So, there's an argument to be made on both sides, and, in the end, it comes down to your preference. If you decide to stick to your guns and use British English, well, no one can fault you. On the other side, if you do decide to try to appeal to an American audience, make sure you choose an American editor (or better still, someone versed in U.S. and UK English) so that you aren't left with any howlers.
What are your thoughts as an author or your preferences as a reader? I'd love to know!