MillyMolly, if a parent's request to start their child a year later is granted by the Headteacher, they then have to re-apply for a space the following year, and be allocated it under the normal admissions arrangements.
So in theory, yes, if the "out of year" child lives closer than a "correct year" child, then the "correct year" child who lives further away could lose out on a space.
Eyeofthestorm - private schools manage it because they bank on the fact that parents will then stay within the private system, possibly in a school which goes all the way through. I don't know if a child moved from one private school to another, whether that agreement would be honoured.
I'm pretty sure that if a child moved from a private/independent school back into the state sector, then they would have to go back to their correct yeargroup.
I'm not sure how old your ds is, but I think that now, if you have the support of the Headteacher, then a delayed year would go ahead. The headteacher has the final say-so, not the Local authority. That's the way it works in my local authority, but I don't know if that's the same everywhere.