Sorry for the delay to your PM. I am, as usual, very busy with school.
First of all, if you come to LBS, do not expect the kind of scholarship which you could get through US schools, which have much larger endowment funds. Although LBS is highly ranked in the FT, its endowment is very low which makes it very unlikely to give out scholarships. Unless you have 760+GMAT, you might not get one. That said, there are however other kind of scholarships you can get. For instance, there are three scholarships given by Deutsche Bank, Citigroup and Merrill Lynch. While the first two are given to women only(20k, 10k), the latter is 10k pounds given to the one who writes the best essay(on an assigned topic). The most important form of scholarship though is the one given by the British Council and Egypt, being a former Commonwealth country, would make you eligible. Just make a google search on the British Council scholarships and you should get there. The scholarship could go for more than 20000 pounds so it's definitely worth it. However, do not rely to much on any kind of scholarships: most students end up self financing their studies anyways.
All things considered, you do have a competitive profile for LBS and there are actually many Egyptians in my program(MSc.). They do bring a wealth of diversity to LBS and it is what makes LBS special in that sense: 95% are non-British students.
FYI, my classmate had 640 on his GMAT but he is in the program. Other parts of his essays were strong and given your strong graduate GPA and 80% range GMAT, you should give it a shot. I agree though that the application fees are quite high but it is a chance to take...
You asked me about the other schools in the PM but I might not be qualified to speak for them. Good luck.