Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
AIRE is a compulsory registration for all Italian citizens living outside Italy required by the Italian Government.
If you have been working in the UK as a permanent employee since January 2015 then you will be liable to UK taxation on your world wide income for the 15/16 tax year et seq. Presumably, as you are employed you will be having Income Tax (IT) and National Insurance (NI) deducted under PAYE. You will also be classed as resident in the UK for tax purposes from January 2015.
There is a Double Taxation Convention between the UK and Italy which precludes the same income stream being taxed in both jurisdictions. This is achieved by means of tax credits, the tax paid in one country being allowed as a tax credit against liability in the other. The Convention does not protect you from differences in rates of taxation, however.
From your UK employment you will receive, at the end of each tax year [5 April] by your employer, a form P60 which sets out the gross income received and relevant deductions. You can use this form to support your tax credits to the Italian taxation authorities. Alternatively, if you are self employed and make Annual Self Assessment Tax Returns HMRC will send you a Form P600 which sets out the IT and NI due which again you can use to satisfy the Italian authorities of the taxes paid in the UK.
I do hope that you have found my reply of assistance.