My ds has passed his 11+ and will (hopefully) go there in September. We are in an area of superselective, so best scores get in, regardless of distance from school.
ds is bright, but not that bright, he will get level 5s at the end of year 6, maybe level 6 in maths, but his school is giving extra help to get that. He goes to a local primary, not in a leafy middle class area.
We did not do the intense tutor thing. I started in Jan year 5, we researched very carefully which tests and then bought the books and worked through the different question types. He found the verbal reasoning easy, and did well.
He does, however, read very well and has a wide interesting vocab. He also is good at maths and well drilled in things like times tables.
I will self tutor dd nest year too, at the moment I am trying to get her really good on times tables and get her to expand her reading a bit.
We found the elevenplus website really helpful. It really tells you exactly what you need to know for your area. unfortunately for you, I think our area is easy than Surrey.
They do say that 11+ is won and lost on vocab, so downloading sets of useful vocab from the 11+ forum and learning 10 per week, is very effective.
It really does mean that you have to commit to 2 or more hours per week work at home, which my ds wasn't very happy about.