On the tradfolk.co site I came across the song 'My Bloke's a Peaky ' as sung by Cecilia Costello . Here is an on-line recording, from the Vaughan Williams Memorial Library of Cecelia talking about the Peaky Blinders and singing the song https://www.vwml.org/record/RoudFS/S369588

Cecelia sings only one verse.

My bloke's a Peaky,
None the worse for that.
He's got bell- bottomed trousers
And a Peaky Blinder's hat.
He's got rings round his fingers,
and round his neck a daf (??)
So all you nosey parkers
Can take it out of that.

Does anyone have more lyrics?
From an on-line post by Jon Wilks I found the suggestion that the song might also be known as " Aye for Saturday Night "