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You don't necessarily need to explain that you are an Italian citizen unless they try to refuse entry. If they stamp your passport with the usual tourist stamp that says you cannot work, that stamp has no legal effect as long as you remain an Italian citizen. This is explicit in the Immigration (EEA) Regulations 2016 in Schedule 3:
Leave under the 1971 Act
- Where a person has leave to enter or remain under the 1971 Act which is subject to conditions and that person also has a right to reside under these Regulations, those conditions do not have effect for as long as the person has that right to reside.
Also, by 11(4), you are entitled to show by means other than a passport or ID card that you are an EU citizen (the following is edited to remove references to circumstances that do not apply to you):
(4) Before an immigration officer refuses admission to the United Kingdom to a person under this regulation because the person does not produce on arrival a [passport or ID card issued by an EEA member state], the immigration officer must provide every reasonable opportunity for the document to be obtained by, or brought to, the person or allow the person to prove by other means that the person isβ
(a) an EEA national;
...
You can of course also have someone send your Italian passport to you, as noted in a comment, but there is a (probably very small) risk of the passport being lost.
I'm not sure whether the bit about leave conditions not having effect will continue to be true after the UK leaves the EU. In principle, it should be, but it's possible that those who have been drafting the new laws have overlooked this part of the old law.