Liberal Democrat leader Nick Clegg said that although he believes civil liberties have been neglected by governments in the pursuit of greater security the urgent challenge being faced by the government means the new data laws are necessary.
In a joint press conference with Prime Minister David Cameron, he said liberty and security must go hand in hand.
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Ministers say the Great Repeal Bill will avoid a "black hole" in the UK's law when we leave the EU. Details are to be published on Thursday.
The triggering of Article 50 has dominated newspaper headlines on Thursday, with many focusing on a possible threat over security by Ms May.
Twelve people have been killed and three injured after a pick-up truck and a church minibus crashed head-on in Texas.