I'll summarise the whole deferring / delaying your summer born / SEN/ premature child's entry into school...
Find out who controls your local schools you are in catchment or interested in. If they are academies or church schools you need to convince their board and the head of the delay to entry of reception. If it's a Local authority controlled school or schools you just apply for the declaration at the normal time of school applications and they will sort it out for all LA controlled schools - much easier. Saying that certain LA's as they call themselves, are open minded and grant this and some aren't.
Consider where you will have your child for the "extra year" my child was at two preschools, one the school nursery would not keep him and the other council one was not keen, they said he had out grown the place. So I had to find a new place, which I did, but I wasn't entirely happy with the setting, but run down. If they are changing nurseries, for just a year would it be better to just start school?
View the schools as usual. Apply as usual.
You will then fill out a form for the declaration if LA. If granted you will be able to withdraw at a later date and still have your school place. Children can change so much in a short amount of time.
Decide what evidence you are going to present to convince your LA and/ or school head that your child should be allowed to enter reception a year later than their cohort. Any issues with documentation like speech assessments, hearing, any medical conditions or additional needs. Now in theory you do not have to have any reason to delay, but this is on the forms and of course you can exercise your rights by just saying "because I want to." If no paperwork or conditions they often consider emotional maturity, issues with separation, confidence, toileting.
Think it through, is it best for your child? You will meet so much resistance to delaying. You will certainly be told but most heads they can support a summer born.
I was granted the declaration of my child and in the end I sent him to school on time. He has done really well, but really struggles with tiredness and separation still in year 1. Did I do the right thing. I don't know, no, maybe I wish I had delayed, but everyone was against it preschool, my family, DPs family, other parents get very funny.
In my personal opinion you should not start your child part time as they will miss so much. The learning of phonics for example is much more complicated than just letter sounds that may have been covered in preschool. They will be covering the blends ( diagraphs and triagraphs ) plus all the repetition of the sight words and numbers. Sometimes it's the terminology that is used at school is so different to how we might play with them ( Number bonds, number sentences. ) Reception is magical and they learn just from being around other and soaking it in.
Other considerations if you delay is age based clubs/ sports , not being with school year. If you stay in area your child should not be asked to skip a year to "catch up" but some issues can arise if moving areas to a less informed LA, especially on the move to secondary. However things are progressing, this was not part of my decision.
BTW I was really worried about the transition into year one, but on deciding to send him I worked very hard with supporting his learning in year R and he's doing fine academically. But there is more to a child than academics, he misses his toys, he's tired, emotional.