Retreating to the Red Sea seems like a good option. The downside seems to me that Italy can block the British way into the Med. At Gibraltar British options seem more attractive:
1. Converging with the US fleet
2. Threatening to land in Italy or France
3. Pressure on the Italian fleet
4. Landing you airforce to help in the above mentioned
I agree. Add to that list that by bringing the planes closer to the UK you make Sea Lion a lot more difficult, which allows you to avoid “turtle infantry builds”. The airbase at Gibraltar (depends on where the German air is located) has long term benefits. It’s a tremendous force multiplier (protects 91 and 92 with same units). You can reinforce Egypt immediately with air.
If Germany makes a build that isn’t suited to Sea Lion, then it seems better to simply strike 97 to finish the Italians (goes long way to secure Egypt) and scratch the German air force.