Regarding the original query, you don't need to have done Economics or indeed History at undergrad level (though both obviously help - I did Economics and History at undergraduate level). Last year on the LSE Economic History MSc course there were many students who had done Politics, IR and a General Course (at a US uni) so it's not vital to have have undergrad degrees in those area. However, you really need to do some general reading about basic economics and the methodology of Economic History (i.e traditional Economic History vs New Economic History vs Institutionalist Economic History).
nb: it looks like Londo took the course during 2003/4 or earlier. My year (2004/5) were the first to have EH400 split into two half modules; EH401 and EH402, the latter being optional (though not for me since I did the EH (Res) degree.