London -- The morning after a 29-year-old man allegedly crashed his silver Ford Fiesta outside the Houses of Parliament, authorities are discussing the possibility of making the area a car-free zone.Speaking on Wednesday to Sky News , Transport Secretary Chris Grayling said "there may well be a case" for making parts of Westminster pedestrian-only."We've got to do that carefully. We shouldn't just take an on-the-hoof response to what was a very disturbing incident," Grayling told Sky News.On Tuesday, a man allegedly drove into a group of cyclists and crashed into the barriers outside the Houses of Parliament. Two people, a man and a woman, were taken to the hospital, while a third person was treated at the scene for minor injuries, authorities said. None of the injuries were life-threatening.Police said that the driver, a U.K. national originally from Sudan whom they have not named, was arrested on suspicion of the commission, preparation, and instigation of acts of terrorism as well as attempted murder. He remains in custody at a south London police station, authorities said.Speaking to LBC Radio in London, Metropolitan Police Commissioner Cressida Dick said she expects to discuss the issue of making the area around the Houses of Parliament car-free with security services."You will notice that the security around parliament -- both in terms of armed officers and police officers and physical barriers -- has been further enhanced over the last several months and there is more to come on that in further months," Dick told LBC Radio.Dick added that the matter would be discussed "parliamentary authorities, us, the intelligence agencies and indeed the local authorities and the mayor."For his part, London Mayor Sadiq Khan told ITV Wednesday that he supported plans to ban cars in the area."I've been an advocate for a while now of part-pedestrianizing Parliament Square, but making sure we don't lose the wonderful thing about our democracy, which is people having access to parliamentarians, people being able to lobby Parliament, visitors being able to come and visit Parliament," Khan told the channel.Former London Mayor Ken Livingstone backed a $22 million plan to partially restrict traffic around Parliament Square in 2007 in time for the 2012 Olympics, but his successor, Boris Johnson, tossed out the plans, claiming it would cause congestion.In an interview with Talk Radio Tuesday, Conservative MP Nigel Evans also called for the area to be pedestrianized to "protect politicians," adding that Tuesday's attack "would certainly ignite the debate" over such plans again.Cressida Dick, the Scotland Yard boss, said it is about taking "reasonable measures" to protect popular sites in the city."The terrorists want us to completely change our way of life, they want us to be afraid and they want us to stop doing what we want to do to lead a normal life in the U.K. We're not going to give in. We're not going to just change our lifestyle," Dick told LBC Radio "But it is important that we take reasonable measures -- as I think we have been doing over the last several months -- to try to make sure that the most iconic sites, including those in Central London, are well protected and if something does happen there, then the police are able to respond very quickly with armed officers, which is what we saw yesterday," Dick added.