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 band of heavy, thundery showers continues to move northwards through this evening, dying away overnight.
The Duke of Cambridge also laid a wreath to honour the victims before kick-off.
The mother of one of the Manchester attack victims has told of the distressing moment she found her daughter being treated after the attack.