It is not necessary to move in order to study. There are many types of distance learning, online programmes. However, mostly they offer dubious quality and aren’t even accredited, sometimes even when they are linked to a particular university. However, you can find good quality online courses as well.
Some are offered by the University of London. Here, it is possible to study the whole course online, but you do have the option to take part in London tutorials. Another opportunity is offered by The Open University. This institution was specifically founded by the UK government to offer distance learning courses. In this case, you cannot study purely online, there is the requirement to sit through some tutorials. But you don’t necessarily need to fly to the UK, these are offered in several regions in the world.
In the US, online courses are offered by Harvard University, for example.
Study for free!
If you don’t insist on getting a diploma, it is actually not difficult to study at all. Many top universities now put their study materials and lectures online. The best known is Harvard and MIT’s Open Learning Initiative and its edX platform. Lecture videos can be accessed by anyone, in order to actually study you have to register (for free).