When instituting a price for a formerly free good, just like when raising a good's price, there is an expectation that you'll lose some consumers. So when UK's The Guardian newspaper put their Sunday tabloid The Sun's online edition behind a paywall, I'm sure they expected some decline in online readership.
With more than a month behind a paywall, independent metrics firm SimilarWeb found that monthly site visits fell from 37.3 million the month before, to 14.4 million in August - a decline of 62.4%. More critically, average time on the site also fell by two-thirds (from 3.6 minutes to just over 1 minute); and more than two-thirds of visitors to the site left without accessing any content. That later stat, called the bounce rate, suggests that those who had an interest in a topic that led them to the site were unwilling to pay the price set by The Sun for access.
Sources - Sun online's disastrous paywall start as traffic plunges by 62%, Greenslade Blog on The Guardian.co.uk
SimilarWeb's website traffic overview for The Sun.