I'm currently a sophomore at university in the U.S. I really want to transfer to a school in the UK (particularly London) but I don't have a super competitive profile.
In general, US freshman/sophomore classes are, to an extent, considered similar to the classes that UK students take from age 16-18 (known as A-levels)... it's hard to say for sure, because it depends on the classes you took and the level of study (i.e. if you took AP or college level classes in high school, this may also be considered equivalent to A-levels), but if you wanted to study in the UK, you might find you have to start a degree from scratch as a first-year student.
The way that UK degrees work is that students apply to study a specific degree programme in a specific department, i.e. English, Mathematics, Geography, etc. (I applied for 'Physics with North American Study' at Exeter University, 'Physics with Astrophysics' at Birmingham University, 'Physics' at Oxford University and 'Physics with Space Science' at Southampton University) and they take classes in only that subject for the entire three years. The first year of the degree doesn't count towards the final degree grade at all (but you must pass all the modules with at least 40%... if you fail a class, and also fail or don't do the re-take exam, then you have to repeat the entire year) and then the second and third year grades are split either 50-50, 33-66, 40-60 or similar. You don't tend to get much choice as to what classes you take within the degree programme either (at least, I didn't in my degree)... the first year is standard for pretty much everyone on the course and then there may be some choice in the second and third years. In the third year, most students will under take a long research project/dissertation project which is written up in thesis form at the end of the degree. A couple of other things that are different from the US system: When you enroll at the university, you enroll for a whole year and for the degree programme... then you will be told which classes you will be taking. You don't register for individual classes and you can't just sign up for classes in any department.
As an example of how things transfer between the US and the UK: I did a Physics degree in the UK and in my second year, we had a US study abroad student in our classes. He was a junior in the US, but was put into second-year classes in the UK. For the third year of my degree, I studied abroad in the US... I went from second year classes in the UK to senior and graduate-level classes in the US.