Governor Linda Hardman said in the letter: "The scheme has become a bureaucratic nightmare which will be repeated term after term. The amount spent on administration would have been of far better use providing new nursery places for three and four-year-olds."
The nursery at Gateway, which is an integral part of the 470-pupil inner-city primary, takes 60 children on a part-time basis and recently received a glowing report from the Office for Standards in Education.
A shortage of places locally, coupled with parents' eagerness to start their children at nursery school, has led to Gateway being oversubscribed for several years.
Headteacher Philip Allen said the voucher scheme, which gives parents Pounds 1,100 to spend on their four-year-olds' nursery education, has done nothing to increase provision. He said: "It's not creating anything for the school - no extra nursery places or extra income. It's simply an administrative burden that we would rather do without."
Many parents mistakenly believe the scheme means extra funding for the school or that it automatically entitles their child to a nursery place.
Nursery and reception-class teachers have had to follow up the applications for vouchers on behalf of parents and liaise with council staff and the Nursery Voucher Centre to supply proof of children's age or residency.
Such was the confusion at the outset that some parents went to high-street stores in the belief that they could exchange their vouchers for children's clothes.
Gateway draws its pupils from a relatively transient population, a factor which has added to the problems with the scheme.
"You expect there to be teething problems, but we ended up acting as middle-man between the authorities and the parents," said Mr Allen. "We had a number of parents who, despite the publicity sent out by Westminster, had neither a nursery voucher nor the required paperwork to get one, so it fell to us to sort out the problem.
"The alternative would have been to turn the children away, which is something we're not prepared to do. But it's just been an enormously time-consuming operation for no benefit as far as we're concerned."
There are fears that the school could end up out of pocket.
Mr Allen said: "Parents turn up to the school without a nursery voucher and without any knowledge of how to get one. So we've had to admit children while trying to track down a voucher. But if the income doesn't materialise there's the worry that the school budget will be cut accordingly."
Westminster heads are, says Mr Allen, unanimous in opposing the scheme. "The difficulties are compounded at larger schools. Because we have 60 children, plus those in reception classes, we have larger administrative problems than most. But everyone I've spoken to is against it because it's extra work for no benefit."
Asked for a remedy to the problems, Mr Allen said: "Put an end to the thing - waste of time."