Both are "correct." I'm not saying this is why, but there are many dialects in British English, so it might be more difficult to pin down what is "correct" compared to American English.

But you would have your essay corrected if you wrote “go put” in any British school (and possibly other ‘commonwealth’ countries) but it’s fine to say it in informal speech; sometimes we hint at ‘and’ by saying the ‘n’ and sometimes we don’t in regional dialects. In the US you would have “go and put” corrected if you wrote it in an essay. So there is a meaningful difference.