Agree with both of the posts from our Italian friend above.
Similar thing exists here (though not so much for tax reasons). By law here you (everyone) is required to register themselves/their address at the local Gemeinde (town or village "office"). And also by law, we all have an ID card ("ID" = Identity). Here, and within most of Europe, showing your ID card (a little plastic credit card-sized thing with your photo on it) will work instead of showing your Passport. Not so much outside Europe.
If you remember, in UK some time back, there was a hullabaloo because the Govt of the day wanted to institute a national ID card system in UK - I forget when, and which party. Doesn't matter really.
That's the ID number the Italian supplier is asking for. As you don't have an ID card in UK, you could give your Passport number, or, if UK driving licences now have photos on them (they didn't in my UK days, long time ago), you could try that. If you don't have either, I GUESS that as suggested above, your NI number would do.
HTH