I have done lots of work on the intelligibility of English in Asia. Within this context, it is worth acknowledging that many accents of English in the UK are not intelligible to other people in the UK. Here is a clip of someone from Scotland, David Linden of the Scottish National Party, asking a question in the UK Parliament (YouTube Link). Paul Beresford, who originates from New Zealand, is completely unable to understand David Linden, even though the latter repeated the question.
Can you understand it?
The question from David Linden is this:
Mr Speaker, I know from speaking to a number of parliamentary colleagues that there are still certain aspects of the estate including the northern estate that are not great for people with disabilities; can I ask the Honourable Gentleman what work is being done to make sure that this place is made more accessible, particularly for some of our colleagues who have a disability.
We should remember that issues of intelligibility are not just found in the context of World Englishes.