About 5 and a half hours.
A random search for flights from Birmingham (BHX) to Cairo (CAI) shows:
OPTION 1: 7hr 35min via Amsterdam (AMS)
BHX - AMS KLM Royal Dutch Airlines Flt 1430 Dep 04:45pm 30Jul,Fri
AMS - CAI KLM Royal Dutch Airlines Flt 553 Dep 09:00pm 30Jul,Fri
Flight Duration: 5hr 30min; Layover Time: 2hr 05min; Total Trip Time: 7hr 35min
OPTION 2: 7hr 50min via Munich (MUC)
BHX - MUC BMI British Midland Airways Flt 3387 Dep 05:15pm 30Jul,Fri
Operated by Lufthansa
MUC - CAI Air Berlin Flt 8896 Dep 10:20pm 30Jul,Fri
Flight Duration: 5hr 35min; Layover Time: 2hr 15min; Total Trip Time: 7hr 50min
OPTION 3: 9hr 45min via Istanbul Ataturk (IST) [Perhaps cheapest option]
BHX - IST THY Turkish Airlines Flt 1970 Dep 02:15pm 30Jul,Fri
IST - CAI THY Turkish Airlines Flt 692 Dep 11:45pm 30Jul,Fri
Flight Duration: 6hr 10min; Layover Time: 3hr 35min; Total Trip Time: 9hr 45min
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