Unfortunately as said in Discover Card's terms, the credit card is not accepted in London, England because it is only accepted in the USA, Canada, Japan, and a few other areas.
Yes, Discover cards are used in most businesses and all over the world. I, myself, have one and use it in many countries. It is easy to get one and they are very reliable.
Hertfordshire is directly north of London, about 50 miles from the centre of town. It depends on where exactly you start and where you want to get to, but would probably involve a train from Euston...