If she is 9 then she is in year 4 and will be taking the 11+ in year 6 so you have a maximum of 1 years tutoring (assuming you are aiming for state GS which have their exams in September). Ds is in year 4 and the norm appears to be starting tutoring at the beginning of year 5 having first checked with a prospective tutor that their dcs are actually capable of passing. Any reputable tutor would do that. No idea about schools in Hampton but certainly in Bucks the best tutors will be booked up by now (some take bookings from year 2 to start in year 5).
Word of mouth is the best way to get a good tutor as there are plenty of not so good agencies seeking to take parents' money.
Where is she academically at the moment? Does she enjoy reading for pleasure? How well does she know her tables?
Without knowing your daughter we have no way of telling whether she needs a tutor for specific help to pass the Tiffin exam, whether she needs help to pass the LEH exam or whether she is not actually academically suited to either school and would go through two years of studying etc to be disappointed. If she is more KGS, Surbiton does she need two years of tutoring to get in or do you simply need to do practice maths & english papers with her (Bonds papers). If she is at a private school ask them whether they feel she needs additional help to get to a particular school.