I am planning to go to Italy for the new school year so I am happy to share what I have found.
Italy is probably one of the few the few places where it is not essential to have completed your degree, but the CELTA is very important, so I suggest you get that under your belt. From doing CELTA, I cannot believe that anyone thinks you can teach without it or that an internet based course will suffice, especially if you have not taught before.
If you look on the job websites, they are still looking for people for the camps so you might get a few weeks there and then you could do your CELTA in Italy and go from there.
Alternatively if you want to spend your summer in the UK they also seem to still be advertising for camps and you could perhaps look for one that is popular with Italians and do your CELTA in the UK, make sure though that you get to Italy in mid August onwards to secure work, in this way doing your CELTA in Italy might be better as you will be building contacts from day 1.
I myself leave tomorrow for 2 weeks for a camp in Italy. The pay may be considered low but I see the benefits of gaining experience, making contacts, and squeezing info and CV tips from current teachers will pay dividends.
The reason I sugget the camps is that when you do CELTA your TPs will be with young adult learners but there is also demand for teaching children and you want to give yourself all the opportunities that you can. Also watching experienced people is an education in itself.
If you do decided to do the CELTA get the books early, I loved the course but as I booked quite late I did not have the luxury of really taking my time and having a good read.
From eveything I have read the pay in Italy seems to be a little lower, but personally some forums (not this one) the teachers seem to be a really strange mix of negative and superior and I am at the point that I think they just want to keep it all to themselves!
I am also being a bit la la la about about the beurocracy, but I think anywhere where you are turning up to live, it is never going to be that easy, I think if you keep that in mind you will be less frustrated.
One of the main reasons I am going over is to learn the language and really explore the country, learn the history - and I imagine those are some of your reasons.
Take advantage of your EU passport and use your year off to explore what you want to do after you get your degree.
I do not know if I can post web links here, but PM if you want some more information.