I'm just putting my hand up to admit that DD1 did have a tutor for a term and a half before she took her 11+. There are essentially two reasons for this:
Firstly, because I thought it best that she be prepared with regards the questions she might be asked and I had no experience of what might appear in the papers or in what format. Of course, I could easily have done this myself, but as a WOHM, I tried and failed. By the time I got home in the evening, made the supper, chatted to DCs and what not, it was too late: she was tired and grumpy, I was tired and grumpy, and we had a major falling-out every time! And we do have a life outside school work! So I decided to pay someone else to do it for me! She wasn't actually taught anything, but the tutor would do an exam paper with her every week so she was familiar with the format. She was in the state sector so there was no preparation at all in class for children who might be trying for the private sector (and quite rightly, particularly as she was the only one).
Secondly, I bowed to pressure from other people, who sucked their teeth and said: "Oooooh, she'll need to be tutored, you know"!
I'm just admitting to this because I wouldn't like you to think there was anything to be ashamed about when tutoring children! I specifically told the tutor beforehand that I didn't want her teaching, because in theory she had already learnt the topics, but that I did want her familiarising with the way an exam paper is presented. I also found the tutor really helpful with regards pitching DD1 for particular schools, by which I mean she was able to confirm that she was capable of getting into a selective school. Likewise, I had asked her to be honest and tell me if I was barking up the wrong tree!
Obviously, the move your DS is doing is different to the 11+, but I guess what I'm trying to say, in a very roundabout manner, is don't be put off by other people's attitudes! There are plenty of selective schools in London and I honestly believe there is a place at one for any child/parent who wants one for whatever reason! I'm pretty sure my DD wasn't the only one sitting for several schools!