I think that this would drastically reduce the amount of money that giffgaff get from data usage. I doubt most people who are using mobile data use it to surf the web. I expect most of them, like you, just use it to check up on facebook, twitter, etc. Also - what would the policy be for websites like stumbleupon, which take you to lots of different websites within the frame of the chosen site? Also most websites take information from different places throughout the web. Part of the reason they can't/won't/are struggling to make the community forums free to us all is because there are twitter feeds and "share" buttons and things which come from other parts of the web.
Also to look at it from a different angle, this would make giffgaff's data prices seem far higher to a third-party onlooker who is thinking of changing to giffgaff.
Whilst I think it's a nice idea, I don't think it would be logically possible as a business move.
However: I could be wrong. 
Good luck all the same.
The Wordsmith
