Stick to the basics. Use ordinary "classroom English." Listeners compensate for an accent by hoping that what they don't hear clearly is guessable. Be as predictable as possible by sticking to the plain English you learned in the classroom. If you try to use slang and colloquialisms ("chuffed," "brilliant," "innit") you will make yourself harder to understand, not easier, because your listeners don't expect to hear those words.

If you are struggling with accents, it’s a good idea to watch some videos online with British accents. Turning on the English subtitles can help you to understanding what they are saying. However there are a variety of different British accents so make sure you choose the one you are struggling with. On a cultural level, in my experience British people tend to have a dry sense of humour and like joking about others and themselves (source: I am half English). Hope this helps!