Been or gone

It isn't correct.

1. They've gone to London. (means they are still in London)
2. They've been to London. (means they have traveled to London and returned)

So, you should write:

They have been to London several times.

I should point out that a lot of native speakers would make this same mistake.

While I agree in a general way TD, I don't think this follows for all dialects or all situations. But it's certainly a good pattern for ESLs to follow.

In American English it's perfectly acceptable.
I am not familiar with any rule that requires "to be" to substitute for "to go" either in the context of the present perfect tense or in the context of the adverbial "several times".
CJ

Dear friends
I quoted this sentence from an English student book,I think It's name was Superstar.
What I say is it was taken from a book.

sorry ,,,,Its name was,,,,,,,,,,,,,,,

Even if you have been to London once in your life time, you could still say:

I have been to London.

You may have made this trip almost 50 years ago. Still you could say I have been to London.

For example, you could tell some friends about the country you have visited by using 'have been' form.

THIS SI TO VERIFY THAT I HAVE BEEN SUPPORTING JOHN HARRIS.