There are three issues here.
One is what is the amount of hours available under a free nursery placement - which is 15, termtime only.
Two - is do you need additional childcare over and above the 15 hours if so then the LA may have a scheme to fund 1:1 on the same basis as the first 15 hours eg my LA offer up to 30 hours termtime only with max. of 75% 1:1 (this was without a statement). LAs have a duty under the Childcare Act to provide sufficient childcare for disabled children, but few do. As you can see even my LA scheme does not cover holidays.
Three is how much education is your child entitled to. As a child with SEN this is based on need not on nursery hours. We get (won at tribunal) 35 hours a week specialist (ABA) teaching 48 weeks per year and my son got this at 3.10 (after 18 months of arguing with LA). If your child's SEN cannot be met within 15 hours then you are entitled to more. For eg had my child been offered a place at the nursery attached to the special school (we were refused) then their standard nursery placement is 3 full day ie 19 hours a week.
People assume that special educational provision has to be limited to the free nursery place, but it doesn't it should be dependent on what your child needs. In our case my son would never have been able to cover everything he had to learn at the pace he learns in 15 hours a week termtime only.
So you should name the specialist nursery and the amount of hours you think he needs to go and negotiate from there.
There is no actual evidence which says 15 hours is the right amount. In USA the guidance is minimum of 25 hours specialist teaching per week topped up by parents. SEN officers have jumped on the free nursery places and call this special educational provision because its convenient but in many cases mainstream nursery places are not education, they are just glorified childcare. If your child, as mine, needs daily specialised teaching of more than 15 hours then this is what should be on the statement.
However you may have to get an indep ed psych to say that if they don't agree and you end up at tribunal