Speaking to the Evening Standard, Zeba Begun, whose house overlooks the scene where the woman died said:
"She then looked to her left and then to her right and I had no idea what she was going to do, I thought maybe she was joking about, but then about 30 seconds later I heard some beeps from the oncoming traffic which could see her.
"And she just waved at the traffic and then fell down onto the road. As soon as I saw it I called the ambulance and police."
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In a wide-ranging Peston on Sunday interview, he said Parliament security needs reviewing and the PM's counter-terror strategy is flawed.
The terror attack carried out by Khalid Masood at Westminster that left four people dead lasted less than two minutes say police.
Two knives were found at the scene in Islington, North London, and the suspects fled on foot before being arrested.