Yeah your NAVs will be more effective with some of their techs (naval strike and the 39' air torpedo tech) and also bringing 2-4 or even 5 if you have that many (may be a challenge for Italy).
I've never had much success fighting France *and* the UK - but usually you can manage with the UK by keeping your fleet *out* of the ocean.
You'll want to do a few things.
1. Send out the subs (groups of 3 is a little big but it should be ok - I prefer 2 because especially level 1-2 subs are really easy for many of the UK's screens to find).
2. wait
3. wait some more
4. Continue to wait - or take Corsica (I prefer to do this with airborne)
5. France dies - send the fleet to Africa to aid whatever troops you have in Libya already in taking the Suez. If you manage to get the Suez and Alexandria, that's the end of the British on the Eastern side of the med for all intents and purposes once you take care of Cyprus and Palestine. As soon as your troops make landfall, move the fleet to port- they can't really afford to stay at sea.
6. Let the land troops capture Palestine and Iraq and push a bit into Sudan if you please.
7. load 4-5 divisions, and rebase to Sardinia.
8. If you can't reach Gibraltar, start shedding older units who are limiting your range. It doesn't matter if your whole fleet dies here - so long as your soldiers take Gibraltar
You should now own the med. You can sail around now killing the remaining bits of the British Fleet - you can also use the supply map mode to find some of their subs. It is possible that you may've trapped a *ton* of the UK fleet in the med - I've had fleets large enough floating around without fuel or supplies that were so massive I was unable to defeat them with the starting ITA fleet - but it doesn't really matter, fight them a few times, get some EXP on your admiral and call it a day (or NAV bomb them until your air general maxes out his level. The starting Regia Marina is good enough (more screens is even better) - it can't go toe to toe with the UK's fleets, but it *can* get you to where you're going and live to talk about the nice little trip they took so long as you're careful with them lol.
Now if you intend to take out the UK you'll definitely have to spend time *at least* building lots and lots of transports and at least new DDs. If you only intend to help Germany by way of landings in the black sea area - you shouldn't need to build any more navy for a while.