I think it really depends where you live, how many grammar schools there are and how much money the locals have.
SW London is very, very wealthy so top Indy schools are extremely competitive. I had to listen to a friend at the weekend complaining about how wealthy her son's friends at St Pauls are and they live in a £5million house in Richmond! Everyone likes to assume that all rich kids are stupid, but its really not true, most of the very wealthy parents I know are Oxbridge and have really bright children, who are also fantasic at sports and really nice kids - life isn't meant to be fair. There are an awful lot of people to whom the cost of private education is a very small expense.
I am told by the mothers that Surbiton prep, very unflashy 11+prep, got 6 into Tiffin boys last year and a few into Sutton Grammars, but only got one of the boys wait-listed for Kings College in Wimbledon. Kings should be easier to get into than Westminster and usually St Pauls (when its not a building site). Having said that I think they pretty much all got offers from Hampton, and all the other local Indy schools.
I've always assumed that it must be really easy to get into a top Kent Indy because they have so many grammars, but was put straight by a poster on this site. Its probably because there's too much money rattling around in Kent.
Sorry and I forgot to say that I know lots of really bright kids who didn't get Tiffin, but who get places at one of the local Indys, but then they don't always get the Indy they want. It all depends on how you do on the day, its a bit of a lottery and if you have a consortium of schools pooling an exam that only gives you one chance to balls up. If you have a bright child who sits for 6 good Indy schools and messes up 2 exams, they still have 4 offers!