Many of those plans have been criticised by internet companies, who argue that such undertakings would require them to put their customers safety in danger and undermine their businesses. It might not even be possible to comply with such rules, they have argued, since laws in other countries explicitly prohibit such measures.
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Now Ms May says that she won't rule out simply "taking down" the "rogue internet companies" like China has.
"I think what we need to do is see how we can regulate," she told the Evening Standard, in response to a question on restrictions on the internet.
The prime minister was then asked if she would rule out "Chinese-style cyber-blocking action".
She only said that she would "work with the companies" and gave no explicit commitment that she wouldn't introduce censorship and restriction regimes like the ones that operate in China.
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