The iambs are fine. Very good, in fact -- you're going to have trouble getting that meter out of your head now 
The language is what really makes this poem work. It's casual and the vernacular makes for interesting rhymes, so that you have a very unique kind of rondeau. There are only a couple of very small things I would suggest changes to. The first is the punctuation in the first stanza, which I think I'd prefer to see as something like:
My father didn't call me son,
he wanted mum to be a nun.
Alas her legs did not stay shut;
the village branded her a slut
and out i popped, the bakers bun.
And the only other thing I have is the last two lines, which would work better both grammatically and metrically if they read:
He doesn't want to share my fun,
my father.
Excellent marriage of form and subject, Billy.
The language is what really makes this poem work. It's casual and the vernacular makes for interesting rhymes, so that you have a very unique kind of rondeau. There are only a couple of very small things I would suggest changes to. The first is the punctuation in the first stanza, which I think I'd prefer to see as something like:
My father didn't call me son,
he wanted mum to be a nun.
Alas her legs did not stay shut;
the village branded her a slut
and out i popped, the bakers bun.
And the only other thing I have is the last two lines, which would work better both grammatically and metrically if they read:
He doesn't want to share my fun,
my father.
Excellent marriage of form and subject, Billy.
It could be worse