The adverts usually belong to the company / product being advertised. The ad agency is responsible for the idea and campaign but are being paid by the company advertsing, so the rights still belong to the company / product.
As for BBC (or any other tv company ) showing adverts as examples of rip off merchchants, it can be argued that the adverts are in the public domain (such as off air broadcasts or more recently Youtube postings) and so are free to be used as examples of how these cowboys work. Same can be said of leaflets or newspaper adverts.
The companies could complain about their adverts being used in this way , but as they are already under investigation for alleged dodgy practices not many seem to bother.
One example is the now defunct Accident Group (Where there's blame , there's a claim) advert used to illustrate the friendly face of what has turned out to be a really bad employer. The company sacked it's workforce in 2003 with a text message and locked them out of their Machester offices.