Given London's location and its extensive rail and air travel networks it's easy to travel to the rest of the United Kingdom and Europe cheaply. While it's tempting to spend as much time as possible traveling during the semester, it's important to balance the amount of time you travel with the amount of time you spend experiencing London and the rest of the United Kingdom. If you get involved with student activities and/or are keen to experience London and the UK during the semester, you might want to consider arriving in Europe before your semester or staying after to do the bulk of your traveling then.
The links to follow have been found useful by past students when planning travel. While these are not endorsements for any particular travel companies, they represent the possibilites for travel from London.
Travel within London
Travel in the UK
Travel in Europe