UK Immigration Law
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Thanks for your question.
You would not be eligible to apply to be naturalised as a UK national because you must be free of immigration time restrictions in order to do this. If you are her on the basis of EEA rights (ie. Your wife) then this means you must hold Permanent Residence. Essentially this is ILR by another name.
IN order to apply for PR you and your wife must have been in the UK for a continuous period of 5 years (with short absences permitted), You must have both been exercising treaty rights, which means either by working in an employed or self-employed capacity, studying or otherwise being self-sufficient.
On the facts as you have explained and with the documentation you refer to you are eligible to apply for PR. You would have to apply using UKBA form EEA4
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I will answer your follow up questions you may have.
It's "Permanent Residence" that you are eligible to apply for. It's slightly different to ILR which is for person here on other visas (ie. non EEA based leave to remain).
Provided your wife has complied with her tax responsibilities it will not matter that she is below the threshold provided that you can show she was working and was otherwise self-sufficient (ie. not claiming public funds).
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