Hi Shaun, glad it's not just you - this is a predicament we've pondered too.
We don't know if Martha was his mother - as far we know, yes she is and that he never had a step mother. It would have meant Harry was 11 years older than his brother Sid - quite a difference. Was he born out of wedlock to Henry and Martha? Maybe. We just aren't sure.
It's all very odd. But as far as we know, he never had a step father/mother etc but it's a possibility. They seem to have moved around quite a bit too.