LONDON—The acquisition of Manchester City by an Abu Dhabi royal was always much more than a billionaire buying himself a shiny foreign toy. From the very start, the project was the tip of a soft-power campaign to entrench the tiny Emirate deep in the British economy. Now, 18 years later, it has emerged that the club was at the heart of the largest cheating scheme in English soccer history. And as City, which denies any wrongdoing, awaits an unprecedented penalty for financial doping, the scandal has rippled all the way to new Prime Minister Andy Burnham. The predicament is especially…