I have to commute to London and I am really fed up with the behaviour of people on the train who cough all over me. Am I right in thinking this could give me sore throats or chest infections?

Absolutely. I am astonished by the dreadful manners of some train passengers, who cough and sneeze over other commuters. If somebody starts doing this to you, the best thing is to move away to another part of the carriage. If that's impossible, put a large hanky over your mouth and nose.