There are lots on here beyond the 11+ phase. You may also want to browse the sixth form thread
viewforum.php?f=57I am not from your area but would say that whilst broadly it is the grammars that do Latin it isn’t solely so you may be able to cast your net wider. At Sixth form the majority schools become selective in some way. There is a lot of movement in our area beteeen, into and out of grammar schools at this stage.
Some schools that don’t do Latin still have Classical Civilisation as an A level which might be of interest your DD? Do you also have schools on your area doing the IB? If your Daughter has a spread of interests it may suit her better?