No file sharing is not illegal, however, downloading copyright material in the UK is a civil offence, that is the copyright holder can sue you with every confidence of success but the police cannot arrest you. There are continuous rumblings from government that they would like to make copyright infringement criminal but the current thinking is to force ISPs to police the whole thing.
In other jurisdictions, the USA for example, downloading copyright material is a criminal offence.
Uploading or distributing copyright material is a crime in the UK and there are examples that suggest that although they are not in themselves interested in prosecutions they will provide police services (arresting officers, search warrants, forensic examinations and so on) to music industry representatives, often on no more than unfounded suspicion. For example a blog you run has download links to copyright material that were put there by commenters, not you yourself, and the police have provided the necessary services for the record industry representatives to raid, search, remove and illegally examine your property although you are more likely than not to be completely innocent.
There is some added confusion in that some countries don't recognise copyrights from other countries, some simply don't care about infringements and some, like the USA, want to imprison anyone who infringes any copyright.