My DD is also a June baby (four this June), and is due to start Reception in September this year - but I will almost certainly defer, as I think that's too early. I deferred with DS (May b'day) until the term in which he turned five, so he missed the first two terms of Reception, and benefited enormously from extra time at home. But others may benefit from extra time at school. DD has lots of friends who'll be in her class, and may be begging me to send her to school in September!(I should add that, very luckily for us, we're going private, so it's much easier to choose when you want them to start - state schools are, I believe, less flexible if you want to guarantee a place).
DD does two mornings at a little nursery school (a very small and old-fashioned one, not a big nursery), and loves it. DS did the same, working up to 4 mornings by the time he was about to start 'real' school. He wasn't keen - or said he wasn't - but it did curb some of his dictatorial tendencies!! It also gave his sister a bit of time with me on her own, which she needed.
I love(d) having them mostly at home, and don't think there's anything selfish about it. Fortunately, the little nursery school DD goes to is marvellous - if it weren't for that, I'd have been stuck to know what to do beyond playgroups and the like.
I don't think it matters, being the younger ones in the year (I'm an end-of-August b'day, and it was never a problem - though children went to school after their fifth b'days where I lived in the 70s, so the differences may have been less obvious!)
No, they don't finish school any later. And once they're 29 and all their friends are 30, they'll be delighted that they're still in their 20s!!
I don't think you have to put her name down for any (state) schools - I got all the application forms automatically, despite not asking for them, so the council must keep records of births.
Hope this helps!