UK Immigration Law
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If your partner has been in the UK illegally then he can only apply for indefinite leave to remain here once he has been here for 14 years. So if he stays for a further four years he will be eligible to make an application for ILR provided he can prove the length of his stay and will Form SET(O).
However you could both go to Poland, marry there and apply (from Poland) for EEA national family permit. He could then return to the UK as a family member of an EEA national and not face the prospect of deportation.
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