> In the entire history of the hackney carriage (black cab) license - going back to 1662 - I know of only one case of a driver having been prosecuted for rape, about 5 years ago.

Pardon?

John Warboys - a registered black cab driver - was convicted of 12 rapes in 2009, and was thought to have carried out over 100. https://en.wikipedia.org/wiki/John_Worboys

David perry - a registered black cab driver - was convicted of 2 rapes in 2010. http://www.bbc.co.uk/news/uk-england-london-32118391

Edward Chapman - a registered black cab driver - was convicted of rape in 2012. http://www.romfordrecorder.co.uk/news/crime-court/black-cabb...

Musie Asgodom - a registered black cab driver in Sheffield (not all black cabs are in London) - was convicted of 2 rapes in 2012 and failed to overturn his conviction. http://www.thestar.co.uk/news/rapist-sheffield-cab-driver-fa...

I could go on but those were the first 3 or 4 links I found, and even those are in the past 5-8 years.

I dont see how some background checks are going to prevent people from raping someone if the opportunity presents itself. Rapists are rapists regardless of what license they have been given by filling in some forms.