@Silvia2253 the simple answer is that there will be a double tax treaty between the UK and Italy so you will only pay tax once unless the tax rates are vastly different between the two countries. There may however be timing issues for paying/recouping tax as the fiscal years are different.
You really need an accountant that ideally understands both tax regimes as you will need to declare income and tax paid in both places. Who has first dibs on the tax is unclear to me but I suspect it is Italy as that is where the property is located.