Some questionable takes here. LSE is a top target alongside Oxbridge if you want to go anywhere IB/Consulting/Finance/PE. Undergrad prestige is what gets you through the door for interviews. Warwick is still a target, but not a top one. Prestige and placement rates are lower.
However, LSE is way harder to get into. They want a personal statement catered to them, so if you have a lick of management/business in your PS it will lower your odds simply because you are wandering off course. I don't know your GCSE/A-level grades either, but I would recommend you get your offers first then worry about these kinds of things later.