Hi I am a recent grad in America. Is it possible to get an LLM without an official law degree, or are these only applicable for after you get a law degree? For instance, I want to apply to an LLM in Cambridge/Oxford etc, but only have an American undergraduate degree. Thanks!

Yes.

Cambridge: "The Cambridge LLM Admissions Committee will consider applications from those whose first degree is not in Law provided they have substantial relevant professional legal experience or have obtained a professional legal qualification with the equivalent of a First Class result. However, a first degree in Law is the preferred preparation for the Cambridge LLM".

Cited: http://www.llm.law.cam.ac.uk/admissions/admissions-criteria.html

Oxford FAQ: Am I eligible to apply for one of Oxford's postgraduate law programmes?
"For law programmes, everyone with an undergraduate law degree, or equivalent, is eligible to apply; and for Criminology programmes, eligibility extends to cover those with degrees in relevant subjects as well as those with law degrees (typically this means social sciences degrees but on occasion applicants with humanities degrees have been accepted). However, entry is highly competitive. Most people ask this question meaning 'am I likely to get in?' The answer is that if you meet the standards listed in response to the next question, you will be in the running for a place. Unfortunately, that is the only advice we can give you on your prospects of admission. The only way to test the ground is to make an application".

Cited: https://www.law.ox.ac.uk/postgraduate/admitfaqs.php

Question: Why are you applying?

Kind regards.