Thanks, Tipsy and Jess, for your replies.
I live in London E11 and the independents we're looking at (all local) are Forest, Bancroft's and Chigwell. Most people put their children in for all three - first time round I thought this was overkill, but I've learned my lesson. They're all selective, with Bancroft's having a reputation for being the most difficult to get into. We applied to Forest for my daughter, as we like it very much and it's very near to where we live. (It is still my first choice for my son.) We're not at all keen on sending our children to schools further afield because of the commuting and the implications for their social lives.
Tipsy, I've no idea whether any of these schools are 'more lenient' with state school pupils, though I'd be delighted if they were! I certainly think prep school pupils are at a huge advantage, as state schools don't do anything to prepare children for these entrance exams. (Am I right in thinking they're not allowed to?) I'm curious, though - is such a policy of leniency usually official or not? Is it something to discuss with the head? The application form for Forest asks what school your child is currently at, so this is information that's available to the school if they're interested. I didn't hear any mention from the school at any stage of making allowances either for their current school or their age (both my children have summer birthdays, so the weighting of the 11+ results by age is a help).
I don't know of any non-selective independent schools in our area, but I'm keen on selective schools anyway and I do feel that my son (and indeed my daughter, despite our recent disappointment) are bright enough both to get into and to cope well with the average selective independent school.
I can't say whether I would prefer an independent to the grammar, as I haven't visited the boy's grammar yet (it's Ilford County High). I have heard, though, that given the excellent quality of their intake, they don't produce the results they ought, and a comparison with the girls' grammar (Woodford County High) bears this out. Obviously we need to visit Ilford County before we rule it out altogether.
Jess: I'm shocked to hear of children being tutored 2 years to get into Tiffin! Yes, I totally agree that tutoring inflates the 11+ results. Just about everyone tutors, so those who tutor hardest and for longest will make it to the top. I've heard stories about girls at Woodford County High who continue to be tutored long after they've started there, because otherwise they can't keep up. So although I'm prepared to do a year, I wouldn't do more than that. I want my son to be able to cope if and when he gets there.
As regards the differences between 11+ and independent English and Maths papers, I just think that if we're going to invest time and money in tutoring, I'd far rather my children be tutored in English and Maths than VR and NVR! At least then if they don't get a place they've done something that will stand to them wherever they go.