For the BBC News pages I use Waterfox. I only access the iPlayer using Chrome and do the minimal amount of registration to allow it to work - no "preferences".. It is hoped this separation of sources will limit their correlation between what I read and what I watch. Ublock Origin and Ghostery are also employed to filter the data they can filch.
BBC radio is supposed to be licence free - so forcing an iPlayer registration to listen is a bit off..
I pay a TV licence - I would like that to be sufficient for them not to mine my data otherwise for their profit.