Is is necessary to have a good level of English?
Not being able to speak good English is not necessarily a requirement of working in London. Most English people will consider your ability to communicate rather than the correctness of your grammar.

It is important to appear confident with your English, even if you do not fully understand everything.

Improve your English
There are many ways of improving your English in London. Apart from reading and speaking there are many English language schools offering full and part-time English lessons. Piccadilly Group offers English language lessons for all levels at its school in central London.
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