Given that
Blair is reportedly a significant advisor to both the Labour party and some elements of the current government, his influence on current political choices should not be underestimated.
The Blair Institute is the nearest the UK has to an American style 'Policy Unit' - it employs more than 800 people worldwide, with offices in London, New York, San Francisco, Abu Dhabi, Singapore and Accra and it's own conference. These guys have impressively high salaries and impressive contact lists (like Ellison), so their advice carries a great deal of weight, despite being largely unknown by the public.