Liam, regarding finding work internationally -
It is not at all common for a company to bring in a stage manager from another country, but yes, it is done. Stage managers can certainly apply and get jobs in other countries, but you will be responsible for coordinating your visa/immigration paperwork - note that it is very different for every country. (For fun, check out the requirements US citizens to work in Russia sometime. You have to have a prearranged letter from the hotel you're staying at to present to the consulate just for approval to
apply for the visa.) Sometimes the company will provide your travel and/or housing, but this would usually apply to inter-European travels (not US to Europe, or US to Asia, etc). It's just so expensive, you're practically spending the SM fee all over again to bring the SM to your country. When you take gigs in a foreign country, the tax paperwork is elaborate - you should definitely use an accountant at this point. You will be subject to all foreign taxes and fees, so you had better know what they are. You can have someone in the foreign company's finance office explain it to you, of course. The most common way to go international is to get on a tour or cruise, or occasionally to pound the pavement yourself in the international theatre community (opera might offer more opportunities for foreign work in general). Really, you apply for international jobs the same way you apply for domestic jobs. Just be ready to travel (ie have a passport) and be ready to look extra diligently for jobs in a country far far away.
The role of a SM is generally the same from country to country, but backstage protocol (and terminology) are different. While you will basically be undertaking the same responsibilities, procedures will probably be different - be sure you have spoken with the PM to know exactly what is expected of you. There are a few discussions around the site about working in different countries (Italy and the UK specifically). Do I need to say it? - you must speak the language of the country you're working in. There are some great British SM books that are easily available in the US - this might give you an idea of varying job duties.
Cable, opportunities for British students would be pretty much the same as for American students in the US. You are certainly eligible for the same opportunities we discuss around this site. You'd have to secure yourself a student visa to enter the US, and you would not be able to get paid work while visiting the country (that would require a work visa, which is different - see a quick discussion of visas here:
http://smnetwork.org/forum/index.php/topic,840.0.html, or visit
http://travel.state.gov/visa/visa_1750.html). A work-study program through your university's student exchange might be an ideal way for you to get this experience.