Is it worth applying for PhD in the UK without the requested undergraduate average? I hold an Italian bachelor in Computer Science with an average of 80% which resulted in a graduation grade of 91/110, equivalent to a 2:2 in the UK system. I am currently attending a MSc in the UK which will terminate in January and until now I am holding an average of 70% even though I am confident I will manage to get a 1st class or a 2:1 at worse from my studies.

I would like to apply for PhDs, but almost every position requires a first class or an upper second, which I do not have for my bachelor. Is it worth applying anyway? 

My master is still a branch of Computer Science but is not the field I would like to do research in, therefore I do not think an high grade would help me in anyway way. In addition, I will not receive the final mark before April and the project, which is worth 1/3 of my master, will not be publishable before then.
The short answer is you should apply.

Generally speaking, all your previous degrees and grades count towards your application for a PhD. But if you are having strong marks in your Masters, you should definitely try to submit your provisional scores to give an indication of your upward trajectory. Many PhD applicants would be in your similar situation. In many UK institutions, a provisional acceptance may be offered to somebody in your situation where the profile is strong, conditional on the completion of the Masters at a certain level. In other words, the final acceptance will not be offered until all the grades come in.