To help give you some idea of flight times, at a typical speed of 460 kts (TAS), if you could follow a great circle track in nil wind:
LGW to Luxor (HELX / LXR):
- Nautical Miles : 2141.92
- Statute Miles : 2465.41
- Kilometers : 3966.84
- Trip Time : 4:54 (includes 15 minute bias)
LGW to Sharm (HESH / SSH):
- Nautical Miles : 2086.27
- Statute Miles : 2401.35
- Kilometers : 3863.78
- Trip Time : 4:47 (includes 15 minute bias)
Nb. More often than not the outbound sectors will be faster ( tail winds ) than the inbounds ( headwinds ).
Incidentally, the longest UK to Egypt flight I could envisage would be, say...
Belfast (EGAA) to Aswan (HESN):
- Nautical Miles : 2526.36
- Statute Miles : 2907.91
- Kilometers : 4678.83
- Trip Time : 5:44 (includes 15 minute bias)
You can try these figures yourself
here.