Aberamentho
Gnosis
I don't know that the Muslim Brotherhood is Masonic. My own brother joined the local Masonic lodge many years ago (thinking it would aid him in his career), but I don't think he's very active in it anymore.
I'm not sure how we or the British benefit from it, though. Both Britain and the US seem to be at a crossroads and in a bit of a quagmire in both international and domestic politics. I can't speak for Britain, but I know many in the US are getting tired of this nonsense and sending their countrymen to these far-off places to die. Perhaps during the Cold War, there might have been some indirect benefit in keeping the region from falling into Soviet hands, but nowadays, there's no reason to be getting mixed up in the region.
The British got the Arabians to help take down the competition, the Ottoman Empire. That's a gain.
They have access to unlimited, almost, oil and control of the Muslim Holy Land through the House of Saud, who they use TO control S.A.
It pleases their Zionist masters the Rothschilds and their heirs, who control the Central Bank of England and the F.R. to boot.
A bunch more stuff I am sure do they get out of it. But these are the obvious things.