Generally speaking London is a very safe city and LSE is one of the few institutions to maintain a largely open campus.
However, it is always sensible to take precautions. LSE Security have produced a great guide to staying safe on campus and in London more generally.
The British Council's Education UK website offers international students useful safety information and tips on how to make sure that your time in the UK is safe and enjoyable.
In an emergency you can contact LSE Security on 020 7955 6555 or on 666 using an internal phone.