My DC is 31/8 (I couldn't hang on for one more day!!!). To the best of my knowledge, I had no choice in holding DC back for a year.
When we joined the school in Nursery, I was told by a senior teacher it normally takes til around year 2 for the 'younger ones' (April-Aug) to fully catch up. That is taking into consideration we had 2 intakes at the time, so DC only got 7 months in Reception (and 1 whole year in Nursery).
I would agree with this to a certain extent for my DC, who has never been flagged as 'behind' but it took til year 1 to really 'click' with education.
I have asked the question at every parent's eve since Nursery 'can you tell that DC is the youngest in the class, in their achievements and behaviours' the answer has always been no. That is very re-assuring for me/DH. DC is doing really well, is happy and is on course for a 2a in Y2 SATs (despite missing 3 weeks due to illness).
Each child is different though and whilst there are some obvious differences in maturity, had I had the choice, I wouldn't change the year DC is in.
I think it would have been helpful if myself and DH had given DC a little extra encouragement with reading and maths in Reception.
Good luck!