In a statement, Blair said: "Jack's contribution to law and order in Britain and this country's standing in the world is quite simply formidable.
"In 2015, Parliament will lose one of the most able politicians of my generation, but I have no doubt that he will be immensely successful in whatever he turns his hand to next."
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A wet, wintry night in places with rain and hill snow slow to move away from southern Scotland and northern England.
The Westminster terror attack dominates the front pages of Thursday's newspapers.
A timeline of exactly what happened.