I don't think you would receive a rejection letter from LSE now that you already have received an offer from Cambridge and Warwick. So, you'd more likely be attending LSE since it's your first choice school/uni.
However, between Warwick and Cambridge, it's a really tough call to make. If you're international, Cambridge might be the ideal school for you because it is -- like you said -- more globally prestigious. On that basis alone, you should choose Cambridge. I would too if I were on your shoes since I'm Asian and Cambridge is an extremely powerful name in my country. But if you're planning to work in the UK, I wouldn't think it would matter where you'll go between Warwick and Cambridge though. So, in that regard, you should choose the school based on fit. Quality of the program-wise, I don't think there is much of a big difference as these two great schools are powerhouses in academics across all major fields.
As an international student hoping to acquire a postgrad qualification in Finance, I would rank it this way:
1. Cambridge
2. LSE
3. Warwick
Again, that’s base purely on school prestige and not the strength of their programs and the student is international. For British residents/citizens, that could be scrambled depending on the kind of environment you prefer to stay for a year or so. In that case, I would still choose Cambridge then Warwick. I would drop off LSE in a second because I don’t like to study in London.