Hi
As a resident of the UK, you are, by default, taxable on your world-wide income in the UK.
This means that if you undertake overseas employment or self employment work, it is taxable in the UK and should be reported on a self assessment tax return.
If the overseas work is via a contract of employment, then you are employed by the Italian company.
The employer, will need to contact the Italian tax authorities, to seek guidance on how they should tax your Italian employment income.
You would declare the overseas employment income on SA102.
If you are self employed, you would report this as self empoyment income on SA103.
If any Italian tax is payable and is deducted, you would also declare the income and tax paid on SA106, claimning up to 100% foreign tax credit.
All section of a self assessment tax return are declared in pounds sterling only, so you may need to convert from Euros.
Foreign income / capital gains, is criteria for completing a self assessment tax return.
You can register for self assessment at
Check how to register for Self Assessment.