There are a number of complications to consider. For example, if the barman asks "What can I get you?" he initiates the linguistic faux pas and you are invited into his dark world of Americanisms. So if you respond with "Can you get me a beer?" I'm not sure how incorrect that actually is. Also you could be asking for that beer in TGI Friday's and so not sure whether American inspired terminology is acceptable in an American inspired bar. I think the best strategy is to just go to the bar and say "beer please". This is a particularly good method because you can insert any drink of your choice before the word please and it still works.
I think it's OK for the barman to ask this because he can, in fact, get you a beer. Like I say, I've thought about this a great deal.
I am OK with people saying, "could you get me a Carling Black Label please" since it's polite, a realistic expectation and you do indeed actually want him to get/bring you a beer. This is the antithesis of "could I (me me me) get a beer" - probably with a rising inflection.
My preference, much like you suggest, is not to pad the conversation unnecessarily in an attempt to appear that I am somehow cool, just blown in from a meeting on a transatlantic flight.
"A pint of Guiness please"
"For a main I'd like the 12 Bird roast please"
Quite sufficient