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Ms. Gunnarsdottir, the political adviser backing the ban, just hopes the emotional debate around the issue will cool down.

“I think we should be able to discuss the Internet with more depth, without just shouting censorship on the one hand and laissez faire on the other hand,” she said.

“Is it freedom of speech to be able to reach children with very hard-core, brutal material? Is that the freedom of speech we want to protect?”

• Jill Lawless reported from London.