Hi Shivlo
I think that there is a huge amount of spin about these 11+ exams. They are highly competitive (and only likely to get more so with the baby-boomers starting to head to secondary schools next year and beyond) and you do need to do the prep for them with your DC, but it is perfectly possible to do it yourself. However, I would imagine that DIY tutoring vs external tutoring comes down to logistics: other time commitments (whether it is work and/or siblings) and whether studying with the DCs is a battleground in your household or otherwise!
We are on the other side of London to you and had the whole Sutton grammars and Tiffin Boys dilemma. They are all highly competitive, super-selectives too, although I have a feeling that HB and DAO score more highly in league tables. The number of applicants seems to be around 1700, with Sutton Grammar having one of the highest number of applicants per place in the UK (I think it's 14 boys to one place).
Our DS was always a top table child and naturally bright, although not terribly learning-focused in his spare time so we weren't 100% convinced that he would pass (he did pass all three that he took and is currently at one of them!).
We did six months of practice but not OTT. We started him off on the Bond Online tests (which are short and sweet and more quiz-like in approach) doing about 15 - 20 minutes a day during the week and then doing age-appropriate Bond books at the weekends. We didn't teach to tests per se, but went over the papers and explained why/where he went wrong. As the summer holidays approached he was doing half a Bond paper (maths or English) a day and we had by this time run out of Bond papers anyway so were using the NFER ones and a greater variety (which he enjoyed more because they weren't as long!) than we had previously done.
We were lucky because DS likes doing exams and was in a highly academic class (just mixed state school but his class was very bright) with lots of healthy competition. Six out of the 30 got places in semi (three) or super-selective (three) schools and none of them had been tutored to within an inch of their lives.
DS isn't at all fond of reading but can pull a reasonably good essay out of the bag when needed. We were quite in denial about the English side of the tests and know that, had he not got in, this would have been the stumbling block. We certainly didn't spend loads of time coercing him into writing persuasive argument or imaginative composition essays.
We didn't actually put DS in for the Tiffin exams. We felt it seemed to be a rather anomalous exam compared with the other 11+ ones (and as we wanted to have a normal comprehensive as one of our six options, we didn't feel it wise to put six selective schools on DS's CAF). It certainly seems as if a lot of parents put a lot more effort into Tiffin exams, but I'm not sure whether that says more about the parents than the inherent abilities of the DC!
It's a difficult one but I do think that a lot of people are making a lot of money out of tutoring, when many of us are more than capable of doing it ourselves. And the thing is that from what DS has told us, many of the children, despite getting into the best state schools in the UK, are continuing to be tutored even once they've secured places.