rabbitstew - a few points. Firstly, English is not like German or say Arabic - in that your quote;
"Just as people from Southern Germany, Austria and Switzerland have to learn a bit of High German at school in order to be able to understand a single word the other supposed German speakers say to them"
demonstrably makes no sense in English. e can understand perfectly well what is meant when someone says 'I done' instead of 'I did'. Whilst Americans may have needed subtitles to understand Trainspotting (the film) that is a pretty extreme example and relates to two very far away countries, and relates to the accent not the grammar anyway.
Whilst of course I would teach a non-native speaker standard English grammar to begin with, speaking is only one skill they need to master. To survive in the UK their listening skills will neeed to be able to cope with people (ie the vast majority) who do not speak RP - you seem to have failed to understand the difference between productive and recetive use of language.
I'm sure even Xenia understands what her cleaner says without the need for translation - we all understand a range of accents in practice. Whilst I'm not suggesting that Xenia's children learn to speak like her cleaner, her children would be at a distinct disadvantage if they could not understand what the servants were saying without translation. 
Likewise, as long as the cleaner can understand Xenia, then the language has fulfilled its aim ie communication.
Working class accents do not in any way impede communication. I see no evidence from my work as a teacher that those with working class accents lack the ability to communicate appropriately when it matters eg write a formal letter, for example.
There are no logical reasons for prejudice against working class or regional accents - it is just really offensive snobbery. I am shocked if not surprised tht in this day and age people are still tring to justify denying people jobs because they are the wrong caste class, just as I find people who discriminate on grounds of race or gendr offensive. Yes, I know it happens but that is no excuse for trying to mould oneself or on's children to 'fit in'. I would no more try to change a child's accent than I would whiten their skin.