Personally, I've never believed that the 11+ was an effective means of social mobility. Bright middle class children have a massive advantage over bright working class children, in all tests.
The system in Bucks is different from many other areas in that it's an 'opt out' test. Unless you specifically withdraw your child, then s/he will sit the test. The 'pass' mark is now around 90% and this leaves very little scope for making mistakes, or poor time management (average 38 seconds per question).
My approach to tutoring is a combination of Montessori education and sports coaching. Lessons are structured, and distractions reduced to a minimum. The tasks are broken down, analysed and practiced in parts. Then the tasks are reassembled and transitions between tasks worked upon.
When the child sits the test, s/he will know exactly what is required in each of the 21 types of questions, how best to tackle each type and (if necessary) which questions to do first. They will even know how best to fill in the answer sheet to minimise wasted time.
Most of all they are learning the techniques of learning and focus.
Effective tutoring is rather more than simply going through papers, it's about becoming a more effective learner.
A few years ago I had the opportunity to observe a class of Yr6 children doing their familiarisation practice papers at the school where I was a Governor. Those who had been tutored were very obviously better at doing the test, regardless of ability.
For an analogy, think of a fit strong child who has just been taught to swim compared to an equally fit strong child who has been a club swimmer for some time. If you were a betting person, which child would you put your money on?