Thanks for your question.
In order to obtain UK citizenship a non-British national must first apply for indefinite leave to remain. You cannot obtain citizenship without it.
A person with leave to remain in the UK under an ancestry visa must complete 5 years in that category in order to apply for ILR and still meet the ancestry requirements at the time of application:-
If you have been on your ancestry visa for in excess of 5 years and you still meet the requirements then you can apply for ILR by submitting form SET(O) to the UKBA:-
You will see that there are some notes on completing the form:-
Once you have received ILR you can apply for naturalisation as a UK citizen 12 months after the date of your ILR provided you meet the criteria on the following page:-
In particular I would draw your attention to the residential qualifying criteria dealing with the time you may have spent out of the country when on your visa or once you have received ILR, not meeting this criteria is the most common form of defect in a person's application for naturalisation.
Once you have been naturalised and undergone the citizenship ceremony you may apply for a UK passport.
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