Don't know this Bully in the Alley but could it be related to the song of the same name by the Oysterband and included on their album Step Outside (1986), a great "folk-punk" album with, ironically, Bully being probably my least favourite track. Written by Ian Telfer and Johnny Jones of the band,

This is what they told him;

BULLY IN THE ALLEY(Oysterband)
(Ian Telfer and Johnny Jones)

Go down if you must but don't stay long
You're a fool if you trust the kids you play among
Better look sharp on your way home son
There's a bully in the alley wants to spoil your fun
So be ready night and day
Stand up for your right of way
There's a bully in the alley and he'll do his worst
There's a bully in the alley won't fear your curse
There's a bully in the alley Get your boot in first
That's what they told him

If you want to win nothing's really wrong
You're a fool if you trust the men you deal among
Better look out for Number One
Or he'll do you down just to see you run
So be ready night and day, stand up for your right of way
There's a bully in the alley......

Out in the darkness he lies in wait
On each knuckle "hate" and "hate"
What you sow is what reap
And the bully in the alley never sleeps

For liberty we must be strong
You're a fool if you trust this world we live among
Now look sharp till the fight is won
There's a bully in the alley with a bigger gun
There's a bully in the alley........