That, in fact, is not what Sir Keir Starmer said anyway, back in 2012.
Part of what he said was:
The well established right to freedom of expression covers not only speech which is well-received and popular, but also that which is offensive, shocking or disturbing. Just because content in a communication is in bad taste, controversial or unpopular, and may cause offences to individuals or a specific community, that is not in itself sufficient reason to put someone through the court process.
No-one had to follow the link to the offensive picture and tweet and it was in fact a link to another publication, not reproduced on here.
However, it is right that this person has been sacked by the BBC.