Maintenance grant Scottish students

Has anyone got a better maintenance grant from SA As for going to University in London. Daughter has offer of UCL, aware she will need to pay the tuition fees but its the grant from SA AS of £4500 that's causing the problem. English students can claim up to £11,000 for central London. It's as if Scotland don't want their students to leave Scotland. If she managers to get Edn or St Andrews she will stay, but they're hard to secure, only a 1/3 of Scottish students get in.