The scheme entitles you to up to 30 hours per week, within the statutory rules as amended by the local authority, and within the individual nursery's "funded childcare offer". That offer describes how the nursery delivers the hours,and will have been approved by the LA.
I need many areas, including my own, the LA dictates which 38 calendar weeks will be treated as 'funded weeks'. Yes, that's 38 weeks, not 39 weeks, irrespective of whatever schools happen to be doing.
Alternatively, nurseries can use a delivery model called the 'stretched offer'. This averages the funded hours over the whole year, coming to c22 hours per week. This is generally better for parents who don’t enjoy the luxury of long holidays and therefore require all-year-round childcare.
Nurseries can choose the daily times at which they offer this funded childcare/education package. This does not have to coincide with parents' working hours, in just the same way as other care/education institutions such as schools and colleges set their hours without reference to parents.
THe nursery is required to offer the funded hours completely free of charge. They can offer 'additional services' such as extra hours, meals, outings, special classes, etc. for an extra charge. They must not make the use of 'additional services' a condition of delivering the funded hours.
That's just the rules, pure and simple. And as PippaPenny has already intimated, there is a whole debate about how unsustainable the scheme is; the methods being used in an effort to try to help parents; and the long term damage and destruction of the childcare industry that may well ensue.
Personally, I’d say the OP is not being "cheated" and is doing pretty well from the arrangement. Term time only contracts are far from common. Most parents pay for twelve months of childcare, and this particular nursery is losing out on 25% of the earning power of this place. It would be perfectly reasonable if they charged a retainer fee for the school holidays: most do, and some charge full whack.
Also, you’re gaining (not losing) from the 38 week delivery model. If the nursery went with the 'stretched offer' model, they'd be offering just 22 hours per week which equates to less than 4.5 hours per day.