Also, OP, a few of the most competitive American universities and elite four year colleges - we don’t have this concept here, but the education can be extraordinary - now offer financial aid, including to international students, that must be seen to be believed.
I have posted piecemeal about this previously on the Board and it has only increased since. Eg Harvard, Yale, Princeton, U Chicago, Amherst (one of those elite four year colleges), but the list goes on.
EG Harvard: family income to $100K - students get a free ride, to $200K - students get a full tuition waiver. At Princeton and Chicago the respective figures are higher. The upper limits are not cliff edges, either.
Many of these make needs blind awards, meaning you are considered for admission without regard for ability to pay and then the money is found. ( I think my list above is needs blind but I wouldn’t take an oath). Not all that make good aid offers are.
The awards I have written of are grants, not loans. I don’t think it would be prudent for a British student to get caught up in the American loans system.
Anyway, that list is just the tip of a large iceberg. The catch is that admissions to these institutions is incredibly competitive, making Oxbridge look easy. OTOH there is no discrimination against Overseas students and there is some interest in creating an interesting and balanced intake each year.
Where I’m going is: if DC is serious about America, it might be worth one or two sessions with a professional specialising in US uni placements for British students to get the latest updates, and assess their chances for the kind of aid necessary to make this happen.
You need a good one. Perhaps some MumsNetters can advise.