Censoring news never works. At best, it just breeds conspiracy theory; at worst, it creates civil breakdown.
It's interesting to note how the suppression of facts affected civil society in the USSR. It's pretty clear that in some cases, particularly the suppression of information relating to active serial killers, that the suppression meant it took longer for killers to be caught and victims were far more vulnerable than they should have been, so the fatalities were higher.
A British example of this would be the reporting of the Yorkshire Ripper as being a killer of "prostitutes." The thinking behind that was to avoid escalating the already present panic, but, in reality, Sutcliffe killed some women who definitely were not prostitutes and is thought by some to have killed some men as well. It is now thought that this "prostitute" angle may have inadvertently meant some victims may have thought they were safer than they actually were.
I think it is worth wondering how the Westminster events would have been processed at the time by the people concerned if the authorities had suppressed information about Islamist inspired terrorism. Just imagine that we didn't know.
The bridge incident would probably have been processed by pedestrians as a man in an out of control car. That information is then delivered to emergency responders, who then go to respond to a situation where the context is incorrect. You would be expecting a victim rather than a perpetrator, and getting the context wrong is dangerous.
It seems to me that, even in this climate, initial security at the Palace of Westminster didn't immediately realise the crashed car held an armed individual who was ready to stab police in an attack. Otherwise, he would have never got to the point where he was able to stab the unarmed PC.
I do not believe in the suppression of news or information and never have. I also get a bit itchy when people call for the suppression of images. It's not until you see certain things that you realise what actually happened and what it means. My DM worked for years on research into certain genocides and it wasn't until I saw the images that I realised the reality behind the statistics because all of a sudden, you've something you can understand on a very real level. It brings it home to you.