Now I’m going to be thinking of that Sylvester cartoon where he lives in a lighthouse with a Scottish lighthouse keeper.
“Sylvester! There’s a moose loose in the hoose!”
I laughed more than I should have at this.
I can’t speak for elsewhere, but here in North East England, both pronunciations are used: “me” in unstressed positions (“I’ll get me coat”)’ and “my” in stressed positions (“Oi! That’s my coat!”).
My impression is that this used to be more widespread, if not standard, and is simply disguised by different spelling conventions. The vowel sound of “me” (possessive) isn’t necessarily identical to the vowel sound the same speaker would use for “me” (first person). The spelling is simply a convention to differentiate two pronunciations of the word “my”, which writers may not always have thought important, or represented in different ways. Is there much difference in pronunciation between “me lord”, “milord” and “m’lord”?
Also at the end of Helter Skelter where John wails, “I’ve got blisters on me fingers!”
That was Ringo.
Well shiver me timbers!
I often get me Beatles mixed up, too. Same with me beetles.
“Sir, I have heard it asked for in many ways, shapes and forms, but I’ve never heard it in the pluperfect subjunctive before.”
I’ve heard it used ‘that’s me mommy’ so affectionate would be a use I have seen.
“Affectation”, not “affection”.
Is Harry Belafonte from Oop North?
Thanks for that. As a guitarist, I have had blisters on my fingers. If I were a drummer, I would have said “hands”.
“I’m looking for me hat.”
–Tom Reagan,* Miller’s Crossing*
It’s a common quality to a lot of non-prestige dialects.
Or to quote my old Yorkshire shipmate, “I’ll be in me bastid’ cabin 'avin a quiet wank and a kip”. 
Around these parts we would likely use ‘mine’ instead of ‘me’ as the possessive, and if it belongs to you then its ‘thine’ or ‘thy’ or ‘thee’
Get thee booits on - we’re of to mine fer some swalley. (Put your going out clothes - especially your boots - we are going to my local pub for some beer - quantity being the important factor here and not quality)
Note that around these parts we would not make the mistake of using the word ‘mine’ to mean a coal mine because
a)there are no mines left these days
b) Such a place would always be called ‘t’pit’
Also a line from the British remake of Firefly.
I’ve always heard it as “My brain hurts!”
In the dialects where people say “me” for “mine”, is the possessive still understood to be “my” but simply pronounced differently? Would a Liverpudlian or Mancunian actually write the word down as “me”, when they mean the possessive?
It depends on why they are writing. The answer would probably be much the same as it would be if you asked whether people from the American south write “y’all” or “you” - facebook perhaps, formal letter for work probably not.
I think the blisters are from going up and down the slide, or the helter skelter.
Anyway, I hear that line as “my fingers” not “me fingers”. Is there any cite available either way? I suppose I could check Beatles Rock Band, but I’m not sure if that’s authoritative.