The longer answer is "well, kinda, but not really". There have been a couple of convictions, but these were guilty pleas - people who have either been advised incorrectly by their solicitors (most probably because they were not experts in copyright law) or just really did not want to go through a trial.
The copyright industry has tried to completely side-step copyright law entirely and use the offence of "conspiracy to defraud" with very dubious legal basis.
It's been far from common, though. There have only been a handful of attempted prosecutions, and usually only because the copyright industry (via FACT[0]) has leant on the police.
Most recently they've c̶o̶r̶r̶u̶p̶t̶e̶d̶ err, co-opted the City of London Police. This is the force that polices the square-mile City of London in the heart of London (See CGP Grey's excellent video[1] for more about the City of London vs the city called London).
[0] The 'Federation Against Copyright Theft' - an absurd name for an absurd organisation - http://www.fact-uk.org.uk/
http://bgr.com/2014/07/23/vcap-and-illegal-downloads-laws-in...