Vilia, I think it would be more normal to miss Y6 rather than Y7. From what you quote from Surrey, it says that by the end of a Key Stage the child should be in their 'regular' cohort. That wouldn't apply if a child did Y6 with the 'younger' children, then moved straight to Y8. It's more likely that school would try to move the child up into their 'regular' cohort sometime within the Key Stage. Or have them miss Y6.
The difference between missing Y6 and missing Y7 is that the child would start secondary school along with everyone else (rather than joining established year groups); so no problem with admissions (except if you'd be aiming for 11+).
Also, some people say that Y6 is basically a waste of time because it is all about preparing for SATS. Teaching to the test. In fact, I've read of a few people here on MN who choose to Home Educate for Y6 precisely to avoid that. I've also read that many children experience Y7 as a repetition of Y6 - a lot of Y7 seems to be establishing the groundwork that may or may not have been achieved by children in Y6. So from that perspective, it sounds like missing Y6 may not be such a bad option. Academically, you may just avoid a year of teaching to SATS, without too much detriment as everything will be repeated in Y7 anyway. The move to secondary school will involve losing friends and meeting new people anyway, no matter if you stay with your cohort or not.
From that perspective I'd go with Octonaught: Do what's best for your child now, rather than be caved by vague threats that may or may not come to pass (and may not be a terrible thing anyway).
What would put me off in your case is your suspicion that they'll try to move your child 'up' as soon as possible.
My August born DS was ok in reception. Not great - he struggled socially and emotionally and would have been ready for reception by the end of the year really. The year would have been much better spent if he had stayed in his nursery school. But he was ok nevertheless - he got to play and have friends. But he is finding the 'all work no play' of Y1 very off-putting. I can't blame him. He is academically able, differentiation is poor, he is basically being made to sit through three hours or boring repetitive stuff - every morning of the week. That is NOT how a 5yo should be spending his days. He should be running and exploring and getting dirty. All the while having no limits on his learning.
So if your child's school is likely to just move your child up into Y1 half-way through his reception year, then you would have gained very little. Starting reception at just 4 is not really the problem IMO. Starting Y1 at just 5 is. (In many schools anyway.)
However, keep in mind that due to Infant Class Size rules, even if the HT WANTS to move your son up, they may not have the possibility, unless a space becomes available in the year above. That would guarantee him to be able to remain with his 'chosen' cohort at least until the end of Y1, and the earliest he could be moved up would be to skip Y2 and go straight into Y3 (where ICS no longer applies so he could be 31st child).