I absolutely agree with Mike and Tiddlymum - you are uneasy about this person's manner, the tutoring arrangement is unclear, the price is too high and you are being asked to leave your daughter with a man you have never met! Don't do it!!!
As Tiddlymum says, a tutor should be able to tell much more quickly whether your daughter is 11+ material or not - that is why some tutors do an assessment session before taking a child on.
Take a read of this, and if you can't find a reputable tutor by word of mouth, use the information on the Forum to DIY.
As a footnote, the one point on which I disagree with Mike is whether one-to-one tuition, or tuition in small groups is most effective. That very much depends on the individual child, and only you can decide which will be most suitable for your daughter.