One of the uses for the semicolon is to express equivalence. When two sentences express the same thought in different words, from a different perspective or with nuanced variance in meaning, a semicolon is often a good choice.
I am no advocate for people who flout the law; I cannot condone the activities of criminals.
That could easily be two separate sentences, but linking them with a semicolon suggests that you are aware of their equivalence but wish to emphasize that one is not simply a restatement of the other. The second half makes a stronger statement even though it is saying the same thing.
But when the second sentence is an obvious elaboration of the other, or expresses an explanation, a logical outcome, or a product of the former sentence, you might prefer a colon:
I speak and write English fluently: as you can see from my CV, I have lived and worked in the UK for over 5 years.
The statement after the colon is an elaboration. You are supplying supporting evidence for your contention that you have great skill in English.
All this is a matter of style, however. The sentences would work together whether separated by a semicolon, a colon, or even a period.
You may also note that the semicolon is not as popular as it once was. If you are concerned that your audience may perceive you as unpleasantly snobbish, archaic, or pedantic, you may wish to use a different punctuation mark. Most likely, though, no one will pay much attention whichever mark you choose.