Here's the way my daughter did it in a nutshell. (She's American, applied from France at EU rates.)
First, she got the grades. That is the minimum you must accomplish to make the first hurdle.
Second, she had a genuine academic passion that she developed on her own. (Her discipline was archaeology, in which she did several internships, which gave her real experience to write about in her admissions essays. She also read extensively on a focused subject, as it happened on the historical Jesus and the Bible as a tool for archaeology. She could discuss theology, history, and archaeological technique in her interviews and believe me, they grilled her on them.)
Third, she was lucky. Somehow, she got noticed as a person they wanted to teach - and her discipline was one of the ones with a relatively easier admissions rate than, say, medicine or natural sciences. She was also a very accomplished singer, which may have helped as they are looking for chorists (she got a singing scholarship).
I would encourage you to try. Cambridge was everything she expected and more, even if it was not all smooth sailing. Finally, she targeted Oxbridge from the age of 12, kept the goal in mind and did research on how to get in, then worked consistently. Her motivation came from within, we did not impose it, though we did occasionally nudge her back on track.
Best of luck.