I agree with alli. You can get quite a good package from abroad. I got a job based on a phone interview. I did all my negotiations over the phone and through emails and I am quite happy with the package that I have been offered. Saying that, it might also be worthwhile to go out to Dubai and just have a look at the place and what is on offer.
In regards to companies, again, alli is right. I found the recruitment agencies I dealt with through google. It's just the case of doing a search of the job title you are after and the location and then contacting the companies that come up in the search results. Ultimately, you know better what your goals are and what you are after but once you are in contact with the relevent recruitment agencies for your field, they will be able to guide you and give you a much better insight of your field in Dubai and more importantly, give you a realistic view of the salary you can expect to earn. Your basic salary will not be a lot higher than it is in the UK; it is the added extras such as accommdation and transport allowances that pushes up the value of your package.
From personal experience as well, I can say that in any field that you work in, your experience will speak a lot louder than your qualifications. There are a lot of us coming out to Dubai with Msc in our back pockets. What will set you apart from the rest and earn you the high salary you are after is your experience, ability, skills and the way you come across during an interview.