I am sorry for your DD’s experience, OP.
I write as a former STEM admissions tutor in a School with not only Oxbridge rejects but Oxbridge transfers - do know that the place doesn’t suit everyone. In fact DH was a UG Cambridge mathematician who got a Distinction at Part III, but that was the only year that he enjoyed intellectually. He also turned down the chance to do a (funded) PhD there in favour of a red brick that was not so removed from the real world. He has had a great career as an RG Maths professor and at the same level in America.
Do keep in mind the figures from @piisnot3 : DD had only about a 50% chance of clearing the STEP hurdle, as Cambridge set the grade boundaries to control their intake. It would have been a long, stressful summer.
I taught in America for about 15 years and want to second @mathanxiety ’s suggestion of considering American universities if DD is not happy with her British options, although I emphasise that she has excellent ones. Americans don’t specialise from the start snd students must satisfy General Education requirements, so a gap year is not a problem. However there will be essays during the first two years!
The universities that @mathanxiety listed publicise formulas for aid. For example, at Harvard a student with a family income of $100,000 will never write a check, full stop. These 7 universities operate transparently, with similar thresholds, aid systems and parity for international students. But others such as the outstanding (partic for Maths) University of Chicago also offer ‘no loan’ parity to internationals (meaning aid is provided via grants, needs based scholarships and light employment - the last is very common in the US) and appear to be essentially needs blind, if less transparent. The Fulbright Foundation website contains lots of helpful information. (The FF promotes bilateral US-UK education. It is named after Senator William Fulbright. Fulbright Scholarships are v prestigious. I think Bill Clinton took one to Oxford. But I digress)
NB it is the famous public universities such as Berkeley, UCLA, Michigan, etc that are very expensive for internationals, as virtually all aid goes to in-state residents. Too bad as those 3 have great maths also!