Have you tried contacting the UAE Consulate/Embassy in London? They probably have a Commercial Section who may be able to give you some contacts for companies who are undertaking building work there or have a presence in the area. .
I did read an article recently which said that this part of the world has also been hit by the recession and that work on several building projects has either ceased or been scaled back but suspect that like the UK unfortunately, work may be difficult to find.
The other thing to do is perhaps go along to your local library (membership should be free if you're a Council Tax payer, you just have to sign to join up) and ask the Librarian for help in tracking down Commercial Building companies operating in that part of the world. Librarians are trained to be researchers as well and may have access to Magazines, Journals, members of overseas Chambers of Trade & Commerce, etc, which members of the public don't necessarily have. In my experience they often like an unusual project to get their teeth into, and if you tell them why you need the infomation they may be able to be helpful. Good luck anyway.
Good luck anyway.