Large corporations are very concerned about their image.
Look at how much Nike suffered when it's business practices of using sweat shops was revealed.
I rather suspect GO is upping the rhetoric to pressure some of the worst offenders to take action before the government takes action itself
Bit of a shot across the bows - take action or we'll do something you'll like less
And it seems it might be working
http://www.bbc.co.uk/news/business-20580980
Remeber this isn't 'the politics of envy' this is about providing a fair market.
The multinationals in avoiding corporation tax are disadvantaging smaller independants.
A crucial role of government is to regulate markets to stop abuses - I mean they could cancel corporation tax and up VAT - that would have a very similar effect but I doubt it would play very well with the public!