Hi Flora,
You can have a company in the UK, not registered for VAT (Since you are under the threshold), and invoice clients through the company. You will need to pay corporation tax on the profits, but these are lower than Italy.
Also, in terms of paying yourself, you can pay yourself just over £7,000 per year without having to pay any NI or income tax in the UK. If you pay yourself dividends, then you can save even more. I can recommend a book (printed or online PDF) that explains this in detail, but you'll need to PM me for this, as I can't post links on the forum yet.
It would also be a wise move to use accountants in the UK. I am currently using accountants that specialise in small businesses. They cost half of what most accountants charge, and their entire system is online. Can send you details if this is of interest.
Hope this helps