What's the difference between the following?
- I met him in the UK.
- I've met him in the UK.
Does the second sentence mean that the event was happened recently?
What's the difference between the following?
Does the second sentence mean that the event was happened recently?
No, it doesn't necessarily mean that the event happened recently.
The difference between the two is a difference in how the speaker is regarding the event: in some cases they could both be used about the same events.
The second "I've met him in the UK" indicates that the speaker is somehow relating this event to the present, but without more context we can't tell specifically how. The "have met" form might indicate a more recent meeting, it certainly implies that he is still alive ("I met him" does not suggest that he is or isn't alive), it might suggest that he is still travelling, and there are many other possibilities.
Interpretation depends on at least two of the possible meanings of meet in these phrases:
The first sentence could employ either of these meanings. The second sentence would only allow the first interpretation.
Does the second sentence mean that the event was happened recently?
No, it doesn't. There's really no difference in meaning, not when the two statements are listed by themselves, side-by-side. They both infer that you met "him" in the UK at some time(s) in the past.
So, what's the difference? Let's assume that you say these sentences, not by themselves, but as possible answers to a question. Then, one might be strongly preferable to the other, depending on the question that was asked.
Question 1:
Have you ever met him before?
In this case, I think either answer could work fine:
Yes, I met him in the UK.
Yes, I've met him in the UK.
But, Question 2:
Where did you first meet him?
In this case, the better answer is:
I met him in the UK.
(because the implied meaning of the sentence is "I first met him in the UK," and you wouldn't say, "I've first met him in the UK.")