I know that there are a few in the UK, but they only cover UK citizens or residents... are there companies like those offering coverage to non-US resident / non-UK resident people for traveling to places outside the UK and US?

You should be able to get travel health insurance for nonresidents traveling all over the world. But be on notice that none of these policies will cover the preexisting condition.This coverage is far from standard meaning that there are a lot of providers of this coverage and each provider has its own contract. So read the policy carefully before you commit to purchasing. You must understand the policy provisions.There are lots of sources - One that I have experience with is http://www.imglobal.com/

YOU CAN get travel health insurance for nonresidents traveling all over the world. I found interesting information about your answer & THE BEST options here. http://all-insurance-online.blogspot.com/2007/08/specialty-insurance.html

Tom Z is correct in saying these plans will not cover pre-existing conditions, however, you can still qualify for some excellent plans that will cover other emergencies, such as medical evacuation and repatriation, which can cost up to $50,000.00! This is a major comprehensive plan by an A+ rated carrier. Here is a website where you can apply online, that will cover anyone who is leaving their home country and has NO health questions on the application. You can get a million dollar policy for under $1.50 a day! http://www.WorldWideMedical.com