Unfortunately the UK has it very bad, the infection rates and death numbers simply do not lie. They need the vaccine as quick as possible if they want to get any sort of control back over the situation. That article doesn't appear to mention the UK's strategy of delaying the 2nd injection way beyond the manufacturer's recommendation, I'm no viroligist but that smacks of desperation.
I am reasonably confident that the western world will get the vaccine rolled out pretty quickly, the bigger issue is what happens to the rest of the world. I believe that this is a situation where the world has to help each other, it is a bigger issue than political borders, colour of skin, religion, etc.