See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question.
This is another very commonly encountered problem. Where somebody’s here on an H visa, L visa or Green Card and their parents are in India, Pakistan , UK or somewhere else and the child is the only support for the parents and the parents are not eligible for any visa to come to the US . We had actually on immigration.com in our sample cases (http://www.immigration.com/sample-cases) there is some mention on cases like this we have done. It doesn’t mean that they will always be successful but really the law permits for a tourist visa and then continued extension of a tourist visa. Sometimes the USCIS and the State Department might consider it to be an acceptable reason for a parent to live in USA on an extended basis. So if your brother has tried to go to the UK and they have not been able to procure a visa to the UK and you are in USA and you being a Green Card holder of course cannot apply for them until you become a US Citizen. I think it would be a good idea to apply for a tourist visa. Make it clear that they want to come and stay here long term as far as the law allows them to.
Once again it will be a good idea to try that. I am not sure if it will work but it is worth trying. Does the law permit a B-1 and B-2 in these circumstances the answer is “yes”. You can actually disclose to the consulate that your parents are going to USA and intend to stay there as long as the law permits because the son resides in UK.