Many people have said that this word means 'leave it out' or 'don't bother'. We it does mean this but it is also used as a sign of agreement to a situation.
It largely depends on the tone
So it can either mean 'fuck that', 'can't be arsed' or on the other had 'yeah mate', 'lets have some of that'
If said in the negative term it would be said with a lowering in the pitch of voice towards the end of the phrase, if however said in the positive it would be said with a rise in the pitch of the voice towards the end of the phrase.
As well as this in the positive it is accompanied by the whip thing chavs do on the 'that'
Jim: Mate have u got dat new playstation game where ya like kill people
Ben: Yeah mate allow that (pulls off a whip)
-Let it be
-Forget about it
-Don't let it trouble you
-Don't even think about it
-Fuck that shit
-Don't bother with it
-Not now, some other time
-"Allow that bitch, she's rough!"
-"Want some next blast of this Bells, blud? Nah... allow that man, that shit's harsh!"
- "Come we go Wetherspoons, last place open round these ends at this time. init!" -"Allow that! That fucking place is full of old ropey, haggard cunts.