Its amazing what the insulation of things like this can have on people - I was sat working at my desk about 500m from it when it happened, we were looking on the news websites and watching it live but I never really felt threatened. Then I left the office early and wandered out onto Victoria Embankment to see the road shut off and police everywhere and up the road could see the bridge closed off and then it really hits you.
As to the point above, people are being murdered each day in the UK but we do not panic, but when the news channels go mental over it in a battle to be seen the channel with the best coverage it only works to get the point these people are trying to make across. It was ridiculous with reporters ringing MPs inside the building and asking them where they were being moved to, what police were with them, what weapons they were carrying - and the MPs were almost at pains to say what stupid questions to ask of them live on TV whilst it was still ongoing but the reporters didn't relent.