Have a look at his "Practical English Usage", Oxford 2005, p. 291
This is one of the rare occasions when Swan is not correct.
It is one thing to say that this, and other "
so-called 'mistakes' have been normal in standard English for centuries", he goes too far when he then says that they "
are not wrong at all".
Most authorities agree with Barb:
"It is NOT standard when you are the grammatical subject
of the sentence: *Peter and me went to the movies -- Don't use this!"
People who use it are frequently considered less educated than those who don't, and you may lose marks in an examination if you use it. The situation may well change in the next twenty years - its use is spreading - but we are not there yet.