These are the only undergraduate degree programs offered in English in Norway:
:: Bachelor of Arts; Nordic perspective on Politics, Biology & Management at Bodø University College
:: Bachelor in Acting and Sceneography at Østfold University College/Norwegian Theatre Academy
:: Bachelor in Biology at Bodø University College
:: Bachelor in Business Administration (BBA) at BI Norwegian School of Management
:: Bachelor in Development Studies at Norwegian University of Life Sciences (UMB)
:: Bachelor of Shipping and Finance at BI Norwegian School of Management
http://studyinnorway.no/sn/What-can-I-study/Undergraduate-studies
Other courses in English are generally only offered to exchange students who come here to study for one year. To be accepted to any other degree program, fluent Norwegian is required. Most people prove their proficiency through a test called Bergenstesten. It took me a year of full time study to pass the test, despite having fluent Swedish (not as a native language though).
http://norwegianlanguage.info/resource/links/bergenstest.html
A residence permit isn't required for citizens of countries in the EU. You just need to pre-register online, then visit your local police station in Norway with documentation that proves you have the funds to support yourself while here.
http://www.udi.no/Norwegian-Directorate-of-Immigration/Central-topics/Work-and-residence/Work-and-residence-EUEEAEFTA-citizens/Temporary-registration-system-for-EEA-citizens/
Unless you're willing to put at least a year into studying the Norwegian language (many immigrants take 2-3 years), your only options are to come on exchange with a British university, or wait until you've graduated. There are plenty of Master's programs available in English. I highly recommend studying Norwegian meanwhile, though. It would help immensely in finding part-time work and having a good social life. Here's information on how to apply:
http://studyinnorway.no/sn/Study-in-Norway/Admission-Application
Also be aware that Norway is incredibly expensive. Most costs are 2x what they are in the UK, and food is especially expensive.