I think that your interpretation is slightly off and Nielsen might have actual teeth here (again to remind everyone this is UK, in the US Nielsen would be in the wrong). The supermarket owns the database rights to their online store, which it then
exclusively licensed (as far as I know) to Nielsen for re-use of third parties. Regardless of your emotions here (and personally I'm disappointed that this is happening), this is UK law and Nielsen and the supermarkets are correct here. If Trolley instead walked physically in stores and then manually collect the data and bought products to shoot photos of* then they have teeth as they have exerted effort into independently create their own database.
* This is now plain copyright law which raises questions, like if the manufacturer-in-question can stop Trolley from publishing those photos (while Trolley owns the copyright on the photo itself, there are de minimis considerations when it comes to the packaging design which is copyrighted by the manufacturer). It might pass fair dealing though.