It is not usually possible, unless you can prove residency in that country. Ie, if you have residency in the UK, you can usually get your visa in the embassy there, regardless of your own nationality.
That's the bad news.
The good news if if your country to visit does not have an embassy or consulate in your own country, then you are obliged to use one elsewhere.
Basically, if there is an embassy in Poland, you are pretty much obliged to use it. If not (and I'm guessing not, because otherwise why ask?!), then using the one in the UK should work.