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Is the phrase 'It was asked' grammatically correct similarly to 'It was said'?
Comments  
Yes.
Thanks, AlpheccaStars. But then what could possibly be the logical reason for being quite rarely used as it is difficult to locate its usage even with Google?
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'It was said.." is much more common than "it was asked" simply because people very frequently want to quote an anonymous source (e.g folk wisdom, rumor).

It was said that he cheated on his wife. (rumor)

It was said that if you took megadoses of Vitamin C, you would not get a cold.

The situation is much rarer for asking. Typically the object is known and used in the passive voice:

We were asked to turn off our cell phones in the theater.

I was asked to be nicer to Susie.

Examples of ask in past tense, passive voice with subject it - used to refer to a previously mentioned subject, or, less often, as a dummy it.

It was asked in such a way as to stimulate our imagination.

Early in this paper it was asked, "do high school science teachers make better lesson plans than English teachers?"

Of course,

The Mayo Clinic got into this specialized business in 1969 when it (Mayo Clinic) was asked by two local companies to design job-fitness evaluations.

The question was answered almost as soon as it (the question) was asked.
Thanks, AlpheccaStars, your answer is really helpful.

Indeed, I am more interested in the rare use of a dummy it, like when referring to a questionnaire:

It was asked the amount of money the debtor owed.

It was then asked the type of insurance they had.

It was asked, "Who's the winner?"

Then it was asked to evaluate the answers.

It was asked if they were attempting to break the record.

It was asked how much they spend daily.
Indeed, I am more interested in the rare use of a dummy it, like when referring to a questionnaire:

It was asked the amount of money the debtor owed. This is not natural. Instead, we would write: It was asked if the debtor owed any money, and if so, how much.
It was then asked the type of insurance they had. This is not natural. The dummy it does not apply, since the object is known. Instead, we would write: They were asked what type of insurance they had.
It was asked, "Who's the winner?" OK
Then it was asked to evaluate the answers. No, evaluate needs a subject. - They were asked to evaluate the answers.
It was asked if they were attempting to break the record. OK
It was asked how much they spend daily. No - They were asked how much they spend daily.
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It was asked and it was very kindly answered indeed.

Thank you, AlpheccaStars. [F]