If you are applying to Oxford or Cambridge from the US, I would apply to all top schools for my other choices, because you presumably are applying to US schools and don’t need safeties. In general, LSE is the most competitive, but probably not a choice for science. Imperial, Durham,and St. Andrews are reasonable choices.
In general, going to top schools in the US has less prestige, because as mentioned most of it is hooks.Also, financial aid and loans are possible, but it helps to have tuition money. Probably 20% based on straight academics and Ivies and top LACs is accurate. However, some hooks are not elite oriented, like athletics, underrepresented minorities, and geographical quotas. Maybe half of students at some schools have relatives who contributed money. It isn’t totally clear who has a hook, and how much they look at private schools, background, prominent parents, wealth, etc.
The British system pretends to be objective, and is more merit based than the US approach, but it is sort of rigged according to the class system. There isn’t as much of a class system in the US, but there are similar obstacles.