Murphy's grammar (Unit 63D) explains the usage of the structure go -ing: go swimming, go climbing etc. It gives a number of examples:
How often do you go swimming?
When did you last go shopping?
I've never been sailing. (!!)
What is been doing there? To me it should be "I've never sailed." Or if we use the verb go -- "I've never gone sailing." Because there is no be in the go -ing structure.
You are quite right. This sentence does not belong in a discussion of the go VERBing construction. The sentence which should replace it is
I’ve never gone sailing.
Note, however, that this is an editorial mistake, not a grammatical one. The sentence “I've never been sailing” is both idiomatic and formally grammatical. With never, have been VERBing is not merely the negative of the present perfect progressive; it expresses exactly the same thing as have gone VERBing.
The issue is that the question has rearranged the sentence order. One would say:
How often do you go swimming? When did you last go shopping? How often do you go sailing? When did you last go sailing?
Or Even:
How often do you swim? How often do you shop? How often do you sail?
Likewise:
I've never been sailing I've never been shopping I've never been sailing
The "been [verb]" construction is necessary because you are making a predicate nominative which calls for the infinitive form.
