If you have reason to believe that someone is falsely using your identity then you need to report this to the police and provide them with all the evidence and information that you have to help them catch them. This would be the same procedure whether the person was in the UK legally or not. Presumably you have some idea of who it is that has stolen your identity if you believe they are here illegally in which case notify the police. If they have sufficient evidence they can bring criminal proceedings against them and stop them from using your ID.
Try to protect yourself in the meantime by changing your passwords and reporting any unusual activity on your bank accounts/credit cards etc to the bank/credit card company etc.
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