"I've been on an exchange to England and it was great." Is that correct? I am no longer on an exchange but it is an experience that influences the present.
Answering for the sake of the answer being in an answer rather than a comment. The answer has been given somewhat by comments, though further questions occur in the comments as well - I will try to answer everything.
That mixture of present perfect and simple past is absolutely fine. Related sentences or clauses do not have to agree in aspect (perfect, simple, progressive), nor indeed in tense. "I have been to England, and I will go again" is also fine.
Taking your initial examples, "I have been on an exchange..." and "I was on an exchange...", there is a difference between them, but both are fine in a sentence of this structure. I was would be needed if you were responding to a question like "what were you doing in the summer of 2010?", or if you were setting something up like "when I was on an exchange...". Most times that you could use "I have been on...", you could use "I was on...". Sometimes it might seem strange, but it would rarely be incorrect. However, the same cannot be said the other way around. "What were you doing in the summer of 2010?" should not be answered with "I have been on an exchange..."; it would seem a non sequitur.
Taking it more generally, "have been" implies nothing more than an unspecified time in the past (which is why you wouldn't use it about a specified time, for instance), while "was" implies it was in the past and is over, and is appropriate to use in reference to a specific time. Hence "I have been ... in 2010" would (usually) not work, but "I was ... in 2010" would.
It doesn't matter whether things were recent or not. That said, there are idioms that suggest otherwise... "where have you been?" is used when someone is late and hasn't been in touch, to enquire why they were late - where they were when they should have been somewhere. Neither the simple nor perfect aspect implies anything was recent, though if it is still happening the simple past is not appropriate. For instance, if someone asks you (say by email or on the phone) "where were you at 18:00?", the answer will usually be in the same aspect - "I was at home". However, if the speaker is still at home, they will usually then clarify that, despite the use of the simple past, they are still at home - "I was at home. I still am."
Your example of the question about a British accent is entirely correct.