I think it may depend where you are and what availability they have. Our local one is very flexible and will take children for whatever hours suit you, as long as they have the space. They are also great at fitting children in at short notice or keeping them for longer if necessary, which is great if shifts change or you get stuck at work. It's probably best to go and have a chat with your local ones and have a look around to get a feel for the place as well.
Most will have allocated places to those 3 before end of August for this coming academic year and so you may need to wait longer for a place at a state run setting even though the EY Funding will apply to your dd from January.
Excuse my ignorance, I have no idea how the whole childcare thing works in UK and need a bit of help. I'm just beginning to look at preschool for DD who will be 3 in september. DH and I work opposite shifts so we don't have childcare costs at the moment and I would like to send her 2-3 mornings or afternoons a week, I think she would love it. Are council funded preschools/nurseries always 5 days a week? I Have looked at some websites and not seen any mention of part time provision really.