It’s not that focused ECs are required, it was that looking at your range of subjects and your range of ECs no particular area of focus that would link to an area of study jumped out at me. Depth is typically valued over breadth in the UK system.
However, Law is indeed a subject that allows for a range of APs, and if you get 5s on your exams this year you will be over the test hurdles. Both unis have an assessment test (Oxford before interview, Cambridge at interview; examples of both are online), which are mission critical, as are (obviously) the interviews.
Have you spent any time looking at the law courses at Oxford & Cambridge? Are you planning on working in the law in the US/UK/other? if so are you familiar with the requirements for converting the undergrad law degree into a qualification for practice? are you eligible to work in whichever country you have targeted?