Hi you can only get a residents visa in Egypt. You can apply for a 6 m multi entry visa in the UK.
You can get a 3 year renewable residents visa. I got a year one from El Tor which is the nearest governent ( passport ) office to Sharm. So I would imagine you would need to go the nearest in Hurghada.
To be able to work in Egypt you also need proof of an aids test amongst other things.