I'm not a student from England, so I can't talk about UK requirements in the US, but one of my close friends at Uni applied to Harvard out of high school. He didn't get in, but I feel like knowing some of the people you'll be up against when applying to Ivy Leagues. He finished in the 99th percentile of his graduating class (about 350 students), with all advanced placement classes. On his SAT's he got a perfect score. He was on student government, as well as volunteering at a veterinary clinic. He also had a few state academic awards as well. Even with all this he got rejected. The one person from his school to get into Harvard didn't have the marks/extracurricular's he did, but her dad was a senator, and she had multiple relatives who attended previously.
As they say "the hardest thing about harvard is getting in".
Also really consider financials, dependant on exchange rates you'll be looking at 120,000+ GBP for your 4 years (that's just tuition & residence). If you're set on studying maybe do your undergrad at Oxbridge and a masters at an Ivy.