"Is it a bad move to apply for a grad scheme in industry rather than a consulting firm or is the jump to Consulting from Industry possible?"
If you are keen to pursue a career in consulting then of course apply to consulting firms - I assume you are.
But it's a very competitive market and so you need a Plan B, Plan C and Plan D - and for those I would definitely recommend the graduate schemes at major FTSE/other companies. Much of the work will be similar, you will be rotated around different areas to give you a broad overview of the business, and if you do well you will be nicely positioned for a more permanent position in an area of interest to you - maybe corporate strategy, maybe not.
After that, as per Tony's comment above, if you still want to go into consulting then switch post-MBA
The point re only going to a top business school is critical. And to add to that, it may be contentious and is anecdotal, but if targeting the MBB-type firms at a post-MBA level, then I would argue that a background of Unilever/P&G/Nestle/Diageo grad scheme --> a few additional years in a line function is a better profile for getting into a top business school compared to a few years at a Big 4. But that's just my opinion.