With Littorio and Vittorio Veneto present the odds are very much in Italian favour even though there are reports of the Italians having serious dispersion problems with their naval guns - low quality propellant and muzzle interference. But that number of 8-15" guns is so overwhelming that even with a 50% hit rate compared to the very accurate 15"/42 on the British ships will still leave a comfortable superority to the Italians. Next the Vittorio Veneto class was very well protected and even the reconstructed battleships were at a decent level - and all some knots faster than the Valiant's 24-25 knots (what wass the other British battleship?). Valiant would be reasonably protected against the 32cm guns of the reconstructed Italians, but Renown, if/when she arrives, is not. The Italian 15" guns probably was the most powerful 15" gun ever built. The price was a low barrel life, but that is only a problem inbetween battles.
I doubt if a single or even two carriers (with small number of planes onboard) can change the odds. The best they can hope for is slowing the Italian main force enough for the British to escape.
A decisive Italian victory would be most uncomfortable to the British, and might have Churchill fall soon after. If the Germans have some diplomtic sense (which however was a scarce commodity in WWII Germany) they utilise the opportunty to get a peace agreement with the British - almost no matter the price and even if it means telling the Italians to shut up and stay put.
Loosing a couple of old battleships will not make UK defenseless however, five KGVs are in the tube, but the loss of prestige is enormous - and this is even contemporary with the climax of BoB. The Italians will be boasted with self confidence however, and that might make things a lot tougher in the Med. This is also a time when the Americans were uncertain about UK's will or ability to stay in the war.
In such a situation I think a German offer to let the British keep their Empire if they stay out of European affairs (kind of joining the Isolationist Club) could be taken serious in London - and certainly if the predominant signal from Washington is: "You are on your own!".
Regards
Steffen Redbeard