It's hard to find any accurate estimate but some data from
http://www.bbc.co.uk/news/uk-england-41358640 gives some idea of the scale of this even if it can't simply be translated into numbers of jobs at risk.
Uber started operating in 2012 and there's a graph a long way down the link that shows (for London) between 2013 and 2017
Private Hire Licenses went up from 67,000 to 117,700
Taxi licences went down from 25,600 to 21,300