Ok, I'll try and help. If I get things wrong, I'm sure someone will correct me
In the term after they are 3, children are entitled to 12.5 (shortly about to rise to 15) hours of free nursery education. The funding is called the Nursery Education Grant (NEG) This is generally organised as 5 x 2.5 hour sessions ie. 5 mornings or 5 afternoons. Athough some nurseries will allow you to do a mix of whole days and half days.
Local Education Authority (LEA) Nurseries which are attached to schools generally only take children either from the term after they are 3 (sometimes called Rising 4), or in some nurseries, the year before they are due to start school (sometimes called Rising 5).
Some private nurseries also take the NEG funding. Some of these private nurseries provide full day care which is usually 8.00am - 6.00pm. However, you can usually just pay for the hours you choose, so you could do shorter days.
Many full day care nurseries cater for a wider age range which would mean that both your children could be at the same nursery.
If you are looking for a child centred approach, you could try looking for a nursery which follows the Reggio Emilia or Montessori approach. Some of the Highscope style nurseries are also very good.
LEA nurseries do not provide nursery care during the holidays.
From the sounds of things, you may be better off looking for a private nursery which will be open all year round, takes Nursery education grant and offers part time places.
Re school: In most areas of England, children go into the Reception class (sometimes called Foundation 2)the September after they are 4 which means that for children with birthdays in August, they are just 4 when they start school. However, you're right in thinking that it's not statutory to send your child to school until the term after they are 5 (or possibly the September after they are 5 - my mind's gone blank!!).
However, if you choose not to send your child to school the term after they are 4, and opt instead to send them the term after they are 5, if they are summer children, it will mean them completely missing the first year of school, and going straight into year 1. In my opinion, this is not advisable. You would be better off asking the school for a long part time settling in period so that your son still has some time with his class.
I think this is probably the longest post I've ever written. I hope some of it is useful!
I'm a nursery and reception teacher by the way.