There's been a couple of competitions lately advertised on the right hand side in the "Mumsnet Latest" box where I have had this problem. When I click on the link it takes me to an entry form, so far so good. When I complete the form and try to enter the competition it opens a box from Facebook - for instance, with the Book People competition - saying "Engage Sciences would like access to your public profile and friends". If you say no, you can't enter.
Nowhere on the page or in the T&C can I see anything about a) Engage Sciences (the competition is branded as Book People) and b) having to let Facebook do stuff as part of terms of entry to the competition. Or is just it me missing something?