As a current Italian student currently reading Business Management at King's I must say your claims are quite ridiculous, certainly not the course at King's. It pisses me somewhat when people judge things they do not really know on the grounds of weak observations and assumptions.
We do not have an actual business school but that's because no college of the University of London has one (apart from LBS, which is, in itself, a business school). We do have a Department of Management though, just like LSE and UCL. Although small, the department is good enough for providing you with all the career and studying resources you need, along with a great business education. The caliber of the staff is absolutely remarkable and you can see that in teaching and courses' structure and content. The number of PhDs from Ivy League schools and Oxbridge working in the department is absolutely impressive.
I had offers from Cass, KCL and Warwick but ultimately opted for King's because, as a university, it is better than Warwick and way ahead of City. In terms of prestige and international recognition, KCL is in its own league compared to the other two, especially City. Also, it is one of the very best unis in the world for social sciences and management, disciplines which of course include Business and Economics. Also, King's is London's most central university, which means you got the world at your doorstep and invaluable exposure to employers.
As to the course, the first year is pretty standard, but from the second one onward you can specialise in the subject you like, whether finance, banking, economics, marketing, accounting, HR. The course offers a very good combination of academic rigour and practical focus and, as long as you put the work in, it will give you the opportunity to get the City job you want. You can also take advantage of a full year abroad on the 2nd year (which will be a replacement year), and spend time at one of top global unis such as The University of Hong Kong, the University of Toronto, UC Berkeley etc.
In terms of preparation for postgraduate studies, the course at King's seems to be great as well. I know 3rd year students who got offers for MSc Finance from ESADE and LSE, MSc Investment and Wealth Management from Imperial, MSc Real Estate Finance from Cambridge...your assetion that "it can't lead to any good master" thus seems quite silly. Also, I wouldn't "guess" that King's masters are useless, since I met people from Warwick and other top british unis who came here for postgrad and did really well in any career afterwards.
Lastly, in terms of career prospects I must say I cannot complain either. The university has an amazing reputation across pretty much all industries and, if you are interested in banking and finance, there are big employers (JP Morgan, Goldman Sachs, hedge funds, investment management firms) coming over all the time, whether for presentations, career fairs or student challenges.
You said you can't speak for Cass because you didn't have enough info and, please, do not do that for King's either because you have no idea of what you're talking about.
Bocconi is a great school and I truly esteem it but you "Bocconians" should really redimension yourself because you are not the only business and finance students in this world and there are people of your same value, if not often much better than you, at quite a few universities around the globe.
Enjoy Milan and, since you are particularly glad of your "Milanese life", do not come to beg for a job here in London after graduation, just like many of your university peers do.