[Stooky Bill]

Regarding the car crashing into the gates of Downing Street off Whitehall. Im watching SkyNews and whilst the news is breaking.... They are simply showing a shot of the Palace of Westminster. There are 50 cameras pointed at the WhiteHouse live all day everyday. Im shocked there are no cameras showing at least the gates or even WhiteHall itself. Ive seen more from social media than they have been able to put on screen. Why does UK have a lack of live cameras?

There is one at the top of Millbank Tower which is what the BBC had pointing at Westminster Bridge when the terror attack happened there a few years ago. 

Having permanent live cameras in front of certain buildings would be a pointless expense 99.9999% of the time. Even when it does you couldn't guarantee it could get a good shot of what's happening, you'd have to be very lucky. Cameras on top of tall buildings are of limited use too, ok for something where there's smoke to be seen but normally there'd be buildings in the way of something on the ground. 

I remember hearing that during one of the London bombings someone had the bright idea of getting BBC London's roof top camera to try and film events, they didn't seem to understand that a 6 storey high camera couldn't zoom in on a bus 3 miles away! 

The other answer is in your question... why would they be needed these days - everyone's got cameras in their pockets