Hello again kb101 - some more responses for you, in case they're helpful.
Vineyard information is correct, and this policy is quite normal, but if you are prepared to start at the school on the exact day they have a vacancy, and another closer family turns it down because it's mid-term or mid-year and they are afraid of disrupting their child, then you're basically in. This is exactly how we got a place at Honeywell in Battersea for our eldest at one point (another very oversubscribed school).
Orleans I don't know personally, but you can't go too far wrong in any primary school in your Borough. Orleans' scores sound fine and I would probably expect to use it for my kids if I lived nearby, not least because it is good for children to have local friends when young, not too much frenetic emphasis on homework, etc etc.
The Good Schools Guide is basically a profitable publisher's combination of insider gossip, Government league tables and the impressions of some tours around schools. Some recent editions have editing errors and there are very clear omissions from the Guide for the simple fact that they can't fit any more in there! However it's a useful handy extra to confirm whether your positive instincts about an included school are similar to those of other people.
I was being a little flippant about the second home abroad thing, but there are some negative social pressures involved in using independent schooling that are not often articulated. I think this is related to exponential increases in school fees over the last couple of decades, as well as the demise of the Assisted Places scheme. I am not sure it is entirely healthy for pupils or their parents.
I happen to be an admissions interviewer for one of the Cambridge colleges (amongst other things) and while things vary a bit amongst colleges, one of the things we do is to calculate the average GCSE points score of the applicants' secondary school and compare them to those of the applicant. So if the average was, say, 40% A-C grades and they had 8 straight A grades, we would take them very seriously indeed. Similarly if the average was 100% and the candidate had the same results we would assume they had had a bit more help than in the first type of school and not quite be so impressed with them. We also give candidates a thinking skills test and put them through a standardised interview. We have all been trained in these interviewing techniques so they are consistent across colleges. The interview is meant to test how candidates can mull over an academic problem and argue it in a small group, which is a characteristic of the Cambridge supervision process and the way a great deal of learning gets done as an undergraduate. In my experience this is where state school pupils generally fall down if they are going to - they are simply not used to robust debate and often feel they do not have 'permission' to challenge academic staff intellectually. Similarly it is true that the advice they receive sometimes from their state schools is woefully inadequate - to apply to do English or History at a popular college probably means you stand a 1 in 8 chance of admissions, but if you apply to do, say, Education at a college with modern buildings rather than romantic panelled rooms you are down to a 1 in 4 or 6 and Classics a 1 in 2 or 3 (or sometimes even a 1 in 1 if you are incredibly lucky and have the intellectual capability). So it really does come down to probability as much as academic background.
This is all a long winded way of saying that unless you really want to splash the cash, you are not usually short changing your child by using the state sector in Richmond and other similar well-performing boroughs, but you may need to top things up with a bit of home tutoring, holiday crammer courses or parental coaching if you want your child to have a good post 16+ experience in the medium term.
To find a good secondary, there is something called the London Families of Schools document which is revised annually, and which groups state secondaries according to things like academic attainment and Free School Meals uptake. Groups 1 and 2 contain schools that are really excellent by anyone's standards, usually selective, Voluntary Controlled or Voluntary Aided. Probably best to aim for one of these in the medium term if you don't want to go down the private route - it's what many Labour politicians do!
Being told off now for spending hours on the Internet unsociably, so better go!