Being non-visa national you can easily travel to the UK and apply for EEA2 there. It takes ages to get it but you should receive Certificate of Application within few weeks and this CoA effectively allows you to work legally in the UK (exercising Treaty rights).

 

EEA2 is not FP. Family permit can be obtained in Italy, this will be issued for 6 months. EEA2 can be obtained only within the UK and will be issued for 5 years. That's why I think there is no significant value obtaining FP unless you want to show FP instead of CoA to future employer.

Few years ago it really took few days to get FP. Now they have outsourced visa issuing business to the third party. FP is indeed a type of visa. Rules state that FP is issued for free and on priority basis but that depends on country now. In France it generally takes 5 working days starting from next day when application is submitted. Also, depends where visa issuing office is located, it's definitely not in Venice, they've centralised eveything regionally. I know that Paris and Dortmund are the places for Western and Central EUrope, not sure for Southern. Therefore, if it's in Rome, you might expect up to 10 working days but if it's in Spain or Greece then who knows. That's why I think your best bet is to go directly to the UK. You'll have to loose some time with documents as well - submit EEA2 application as soon as possible, wait for CoA and then request a passport to be sent back.

By the way, I've heard that some employers do not like CoA and having FP is an advantage in this case but that depends on what kind of job you'll be looking for.

 

And some more..

By the way, I've just quickly tried to find where that visa issuing office is located in Italy and it's really in Rome. Check this thread

http://britishexpats.com/forum/showthread.php?t=578814

And this is Home Office advice from their site: Non - EEA family members should get an EEA family permit before they travel to the UK if they are visa nationals, or if they are coming to live with you permanently or on a long-term basis. If they try to enter the UK for this purpose without an EEA family permit, we may refuse them.

Therefore, Home Office would like you to obtain FP before coming to the UK for long-term basis and it seems reasonable. The problem is that British Embassies throughout the world hate Home Office as they are always 'fighting' for power. That's why the system is so clumsy, Home Office says 'Go get FP', the Embassy says 'You don't have to' or the Embassy tries to take its time, asking for some additional docs and trying in other ways to show that Home Office cannot give orders to the Embassy. I've seen it in Paris and got resolution only when emailed both parties (cc and threatened to claim all the costs for travel and accomodation because two parties are contradicting to each other and European Law. That worked but a lot of stress. My advice stays the same, go to the UK directly, just don't say that you've come for work if they ask you at the border. Border Agency is an ally of Home Office if that makes sense, they may kindly ask you to get FP