Is this correct usage of a semi-colon?

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.

It is somewhat of a judgment call. According to Grammar Girl, semicolons are used most commonly to "separate two main clauses that are closely related to each other but that could stand on their own as sentences if you wanted them to."

Your two sentences are related, and I presume you would like to show that living and working in the UK helped you become fluent in English. So, I think the semicolon is fine in your example. Just don't overuse the construction in whatever letter or document you are writing.

(There are some people who might quibble about your use of over instead of more than, but that's a different issue [or non-issue, depending on your viewpoint]).

It's a matter of what the author is trying to convey. Semi-colon is more like a comma but adds more emphasize and a longer pause than comma. With comma it's like taking a breath, while with simi-colon it's more like arching your eyebrow and signaling. Based on my experience, semi-colons are used to connect two closely connected ideas that could fall into separate clauses. It's something stronger than comma but weaker than full-stop. I like John Scalzi's advice on the usage of punctuation:

Periods: When you’re writing down a thought and you’re at the end of that thought, put a period.

Commas: When you’re writing down a thought and you want to take a breath, whether mental or physical, put in a comma.

Semi-colon: Put these in your writing in the place where, in conversation, you’d arch your eyebrow or make some other sort of physical gesture signalling that you want to emphasize a point.

Colon: Use when you want to make an example of something: For example, just like this.

That said, I think in your example you have used it the right way as the two clauses are closely connected and that's what your are trying convey.