@Afrikakorps Mostly agree with Taamvan here – you’ve described an interesting gambit, but it sounds like your opponent fell for your trap by passively consolidating his Italian fleet and leaving it idle.
As other commenters have pointed out, the Axis can completely counter this strategy by using the Germans to clear away blockers, taking Egypt or Gibraltar pretty early and with potentially disastrous results for the British.
Even without German reinforcements, the Italian player can still actively consolidate their fleet by bringing it together in a different sea zone each turn, killing one British unit at a time. Italy-1, you kill a destroyer. Italy-2, you kill a cruiser. Take casualties on your air units or battleships, save your money on Italy’s first turn, and by turn 2 you can build an Italian carrier + sub, or carrier + fighter, or whatever else you need for naval parity. By passing up the opportunity to kill the Italian fleet on UK1, you may lose the opportunity to ever kill off that fleet, and if you follow through with plans to move the entire RAF to the Med, spend part of the UK economy in South Africa / Persia, etc., then Germany will have a free hand in the north Atlantic, and Moscow will be more vulnerable when the Germans are ready to attack it. Basically any time you concentrate the mobile British forces, you need to achieve decisive results within a couple of turns, because events will continue to develop elsewhere on the board, so if you’re merely stalemating the Italians in the Med while losing ground in the Atlantic and Moscow (and perhaps India as well), then you’re not making the right kind of forward progress on the globe as a whole.