Here in Hampshire, it is dealt with by Children's services. They have an Area Inclusion Co-ordinator, who visits and assesses children in the setting, and advise on whether the child requires Early Years Action (i.e. the preschool need to do x, y, & z to help the child) or Early Years Action Plus (x, y, z plus help from outside agencies), and within that they can apply for funding for extra support.
In Hampshire there are 3 rates, I believe:
'Standard' - £8.75 per session to provide funding to enable a child with SEN to access mainstream pre-school.
'Enhanced' - about £12 per session, I think.
'Double' - which I have been told is for children with the most serious needs, such as being completely unable to support themselves, require feeding etc.
DD was assessed in October '08 at 2.10, and given Standard funding until she starts school. But the preschool and the AIC both said she needed 1:1. At first they topped up the funding out of pre-school's own budget to provide full 1:1, but they couldn't afford to do this. So recently they cut her 1:1 time, without telling me, and suddenly she came home with hardly any paintings, I was getting called in because she had had accidents, she was having melt-downs when I came to collect her, etc.
She has been reassessed in March, and the Area Inclusion Co-ordinator has gone back to Children's services and is applying for Enhanced funding for DD, so that she can have the full 1:1 she requires.
She has GDD and no sense of danger, and can't join in group activities without support.
I would perhaps phone your local education authority and ask to speak to someone from early years, to get a feel for what happens in your area.