In my case, I did apply to other colleges since I didn't assume I'd get into the LSE, particularly to study Law, which was highly competitive.
LSE now require significantly better A level grades, than when I applied, at least three A's now. But I'm not sure if that's because the students are higher calibre or because of the grade inflation everyone's been talking about.
Maurice Saatchi got a first at LSE, back when getting a first was very rare. He is also one of the greatest minds in advertising, author of the Iconic 'Labour isn't working' Campaign that ushered Margaret Thatcher and the Conservative Party into power in 1979.
As Maurice said himself, 'I left LSE with my first-class honours degree in economics. They did say to me that I possessed what they called "effortless superiority", and that has always worked very well for me'.
Here's a good piece about how he started in Marketing, working for Michael Heseltine, at Haymarket.
There were prominent MPs, Peers, Academics and Executives from organizations like JP Morgan, HSBC, Fidelity Investments, Barclays Bank, Goldman Sachs, Bank of America Merrill Lynch, AXA, Zurich, Wells Fargo, BP, Mckinsey, PWC, and Accenture, at the event, to name some...
On the river outside the reception, from the House of Lords