11+ Music scholarship...

DD was awarded one (grade 5 cello, grade 3 piano, very strong choral ability), but the competition was fierce and what swung it was her interview after the performance/exam, and the fact that she had a record at prep school of being involved in every group she was eligible for so would be an asset to the school. Apparently she and the music master had a long chat about music used in television commercials. Some of the questions they ask are completely out of left field. Also scholarships are worth hugely varying amounts. For some schools they are almost financially derisory. Kudos only. At others they make a real difference to the fees.

Schools not should and require not reque! Darn spellchecker!

It really depends on the school. Plenty of should outside London would reque grade 3 for 11+ but virtually all in London require grade 5 minimum. At 13+ it is grade 5 but the reality is closer to grade 8 on the first and grade 6 on the second instrument. Choristers are highly sought after and will often take a scholarship if they have a lower grade on an instrument. Then there is current demand at the school so a child playing viola, double bass, French horn or bassoon may be offered a scholarship over a violinist.

What schools are you considering?

Each school will publish guidance on their website and you can often meet the director of music informally ahead of the audition (in fact you should do this to get an idea of what is expected). There will be internal as well as candidates (and it may be easier for the former). Bear in mind the stated required grade - probably grade 5 in first instrument - will be the minimum and many candidates will have achieved higher. General musicianship is also tested (sight reading/aural) and schools will look to see how involved a student is (eg playing in orchestras, singing in choirs etc).

HTH