In case you've ever wondered about it (I certainly have), here's a good explanation of a dry grammar rule from this article:
The "that/which rule" is like the purported prohibition on split infinitives: some people feel strongly about it, and it's thus worth knowing, but it has no real grammatical or stylistic justification. My reason for discussing it is to explain that it's a waste of time to worry about the choice of "that" or "which" as a relative pronoun. Your meaning will be clear with either, so long as you are careful about punctuation.
The rule concerns what are known as relative clauses. Take this sentence: "The article, which the greedy columnist submitted before rushing to the bakery, was full of mistakes." The words between the commas form a relative clause. If you deleted them, the sentence would not only make complete grammatical sense but also convey the essential point that the article was full of mistakes. The clause provides supplementary information about the sentence's subject (namely, the article).
Now consider this sentence: "The newspaper that employs the greedy columnist has run out of blueberry muffins." The words "that employs the greedy columnist" also form a relative clause. But here it's not just additional information: it specifically identifies which newspaper it is that has run out of blueberry muffins.
A relative clause that adds extra information, not essential to understanding the sentence, is called non-restrictive. In the sentence about the error-ridden article, it's separated from the main clause by a pair of commas. These function as a pair of brackets would do.
A relative clause that is essential to determining the reference is known as restrictive. It isn't just any newspaper that has run out of blueberry muffins: it's the one employing the greedy columnist. To denote that the clause is restrictive, there are no commas.
Here's where the "that/which rule" comes in. Some style guides insist on "that" rather than "which" in a restrictive clause, and "which" rather than "that" in a non-restrictive clause. They would hence fault our sentence about Mr Duncan Smith, in which the critics' claim is essential to identifying which sweeping welfare cuts we're talking about.
I don't agree that the relative pronoun "that" is even desirable, let lone necessary, in our sentence. It's unnecessary because the absence of a comma before "which" makes it clear that the clause is restrictive. It's undesirable because we've already used "that" (as a conjunction, reporting Duncan Smith's statement) earlier in the sentence. It would be clumsy to say "that" again, this time as a relative pronoun.