Can you change courses when you are at LSE?Watch
LSE doesn't do an Econ with normal History degree.
You would have to change at the start of the first year, before classes and lectures start properly.
A few people manage to do it, many others don't. You would have to have a very compelling explanation for why you wanted to change, as well as having the grades and subjects (A*AA for Econ rather than AAA for history; you would likely also need to have Further Maths A level).
Basically, you can't rely on being able to change. If doing Econ rather than History is the be all and end all to you, perhaps you should take a gap year and reapply.