David Cameron said the murder of Fusilier Lee Rigby "shows that we have to redouble our efforts to confront the poisonous narrative of extremism and violence that lay behind this and make sure we do everything to beat it in our country."
Speaking to reporters in Brussels, the Prime Minister said: "The whole country was completely shocked by the murder of Lee Rigby and the whole country united in condemnation of what happened."
"I'm sure everyone will welcome these verdicts today," he added.
In her only television interview since the verdict, she told ITV News that she begs forgiveness from Lee Rigby's family.
A mother and daughter who witnessed the attack on Lee Rigby have told ITV News how they are still haunted by what they saw that day.
Lee Rigby's sister told ITV News that she wishes she had not talked her brother out of returning to Afghanistan shortly before his death.