I'd agree that parents can support children themselves without the need for a tutor. However, some children don't respond well to parental input and their hidden anxiety comes out as anger and resistance. For this reason, and so that parents feel reassured that they're on the right tracks in terms of preparation (what to do, how often, etc.), a tutor can be more than handy.
As for preparation, I'd expect a good tutor to be working with your child on something you'd found to be tricky for him/ her (preferably while doing a practice paper/ exercise that they'd set for him/ her to do at home); to teach this concept (one that you may already have tried and failed to get across to your DC) and set some further examples of this and related/ unrelated concepts.
The tutor should be guiding you as to which practice papers, exercises or tests to be doing each week. It's important that your DC is used to the types of questions and format of the tests they'll be sitting.
You may also like to sign up for Mock Exams. These can be alarmingly discouraging but very helpful in terms of getting to know what it's like to sit the exams, neutralising the impact of the test to some extent and feedback so that you can practice the exact question types that your child omitted or made errors with in the mock.
Has your tutor provided you with some basic information such as:
Test types
Practice materials
Breadth of question types - and which your child needs to work on
Recommendations for above (each week)
Your child's timings (are they finishing the paper/s in time?) etc.
By now, despite huge (and very recent) changes in the test formats and contents, your child should ideally have covered most of the mathematics curriculum of Year 6 and beyond, in certain aspects (more advanced ratio & proportion, Fibonacci series, etc.). They should be preparing like mad for the VR (if that's relevant to your area) and beginning to practice with test papers.
Despite their usefulness, a tutor is not necessary, as I said. There's so much available online. What IS necessary is to prepare. Sadly, unlike the school in which I began my teaching career, most schools fail to prepare their students with adequate 11+ booster groups. Those that exist in schools are of the 'too little too late' variety - especially now, when early VR (vocabulary) preparation is becoming paramount. School curriculums do not sufficiently cover the mathematical concepts tested, as much of it is in the Year 6 curriculum (too little, too late by the beginning of September, Y6).
As for the depth and breadth of vocabulary and the VR exercises - these are not taught in the school curriculum unless arising in the odd weekly comprehension. It's inadequate. Schools are aware that some children will be sitting the 11+ exams and I feel that they have a moral obligation to support them with their preparation. However, many schools are 'school centred', interested in their SATS results and not in being child-centred in this respect. Rant over.
In answer to your original post (and back on topic) OP, I'd say that a minimum of 1 hour of weekly work would be appropriate at this time of year - comprising of a combination of a test paper (even if it's a 10 minute test in VR & in maths - depending upon what is tested in your area) AND consolidation (exercises / further questions to practice an aspect that your DC found hard before you/ the tutor helped them in their lesson. In addition to this, if your DC is going to be sitting a CEM VR test, they should be working on something to broaden their vocabulary and spelling.
While there are always those children who 'perform' brilliantly in the test with 'no preparation', these are rare. In fact, I'd not be lulled into a false state of security in assuming that my child would be one of these Sword in the Stone type legendary characters we all hear about. Let me share something with you: I had s tutee who came to me for a year and a half prior to the exams. One evening, as my next tutee waited in the corridor, current tutee's parent arrived to collect them and for feedback. When both parents met in the corridor, one said to the other: "Oh, I thought you said that xxx didn't have a tutor!". It was awkward. It is also a valuable lesson: don't believe the hype or illusion that many parents give. Parents will only tell you of 'their tutor' once you're no longer competition. If it's a good tutor and your friend tells you about them, you've a real friend!
Parents understandably like their children's achievements to be viewed as personal achievements - not a reflection of a good tutor's work. I actually agree with the importance of this principle. It takes us back to the central argument about whether tutors should exist / be used: a child can have the most wonderful tutor but if they are not 'able' enough to score highly, they won't.