Is my Step Daughter eligible for UK Citizenship ?

What you've got here is that she was born too early - unmarried British fathers didn't count until 2006. So she is not a British citizen on that basis, but has several ways to apply for British citizenship by registration (a kind of "naturalisation-lite").

A couple I can immediately think of are that as she WOULD be British if she was born after 2006, she can get British citizenship by registration. Another is that as she has lived in the UK for the first 10 years of her life, she can get it that way.

Maggie who Brother_Hesekiel refers to is a frequent contributor on this site and is an expert on the subject.

But I'm still confused - in 2001, Portugal was a member of the EU, so your step-daughter was born in the UK to a mother allowed permanent residence in the UK, and therefore she should be British by birth and not need to apply for anything. Is it just that you applied for her passport the wrong way?

Do you mean "father" with "farther?"

If so, your step-daughter would have acquired British citizenship via lex soli at the time of her birth, assuming her biological dad was a British citizen at the time she escaped her mom's birth canal and he's on her birth certificate.

If her Portuguese mom had settled (right to abode or ILR) in the Uh-kay by the time the little critter was born, she too would be a British citizen.

I'm afraid you're not telling the whole story here. Perhaps Maggie will chime in later.

As she is born in UK irrespective of her parents marriage she is a citizen of UK. Please check the citizenship law of UK.