That is government funding. Schools maybe reluctant for part-time because of the way they organise their curriculum but from reception age it is not a funding issue. However if there is dual provision, as sometimes happens with SN, the situation can be more complex.
Can anyone answer a general question I've been asked about whether a pupil who is part-time in reception (up to lunchtime only) affects the school's funding. Or, is this subject to which county council the school comes under?