Depends on your definition of 'inexpensive'! Wanting to stay away from Cairo for more than three months puts you into the more expensive fare bracket. Have a play about with the 'flexible dates' option in the UK Travelocity site to see how your options change. I think this link will take you there

If you were away for less than three months you could buy a return LON-CAI for as little as £184+taxes; but raise it to six months and it's £300+ (these are economy fares).

How important is it to get back to CAI at the end? Alternatively, you could do your sightseeing at the start of the trip and forget to use the last coupons from your cheapie-return to CAI from LON, and your DONE. We've all done it.