At the risk of raining on the parade, this is all utter bollocks.
The margin Blair's company is making is about what I'd expect for a professional business. No company discloses all of its admin expenses in its accounts - it would be far too long and dull - but HMRC will expect and can demand a full breakdown. But it doesn't take an expert to work out that the expenses will include depreciation, travel and hotels, entertaining (not tax deductible), interest and other financing charges, the costs of hiring expertise from people who aren't employees, and any number of perfectly legitimate costs.
Blair has already explained that he was advised to set up the partnership structure not by tax experts but by security people. Blair is still one of the highest profile terrorist targets in the world. Partnerships are not required to disclose as much information as companies, so its more secure for his fees to go through partnerships. This is all a matter of record.
Finally, although not relevant to this travesty of an article, remember that as and when Blair takes money out of his company, he'll be taxed on it personally.