Can "would rather" be followed with a past perfect?

Can "would rather" be followed with a past perfect? Can it be used to express a regret, a wish the past had been different?

Example taken from First Certificate Language Practice by Michael Vince, page 43:

I would rather you did not tell John about this.

Neither now, nor later, that is.

How about earlier? "I would rather you had not told John about this."?

Solution 1:

Would rather means

(would rather) Used to indicate one’s preference in a particular matter: would you like some wine, or would you rather stick to sherry? [Oxford Dictionaries Online]

It describes a current preference for something in general or in particular that has not yet happened. As such an object in the form of a clause would not use a past (or past perfect) tense verb form.

If you wish to express your preference for things that have already occurred, the main clause should be put in the past, and rather does not quite work

I would have preferred you had not told John about this.

Solution 2:

Yes: you would use the past perfect to express a wish the past had been different, since the simple past would express a wish for the present or the future. So,

I would rather you had not told John about this

is actually a correctly formed sentence. You can see plenty of examples of sentences from published books using "would rather you had not" (or more commonly "would rather you hadn't") in this way if you do a Google Books search.

According to Cambridge Dictionaries Online, the past simple and past perfect are used with "would rather" in the following circumstances:

When the subjects of the two clauses are different, we often use the past simple to talk about the present or future, and the past perfect to talk about the past:

• I would rather they did something about it instead of just talking about it. (past simple to talk about the present or future)
• Would you rather I wasn’t honest with you? (past simple to talk about the present or future)
  Not: Would you rather I’m not honest with you? or … I won’t be honest with you?
• I’d rather you hadn’t rung me at work. (past perfect to talk about the past)

Incidentally, the BBC also discusses the use with the simple past that you show in the example sentence in your question:

Would rather (but not would prefer to) is also followed by a past tense when we want to involve other people in the action, even though it has a present or future meaning. Study the following:

• Shall we go out for dinner tonight? ~ No, I'd rather we ate at home, if you don't mind.
• Shall I write to Harry and tell him that we've sold the car? ~ I'd rather you didn't.
• My mother would rather we caught the bus, rather than walk home after the party.