Phase 1 of the scheme 'goes live' this week as four-year olds begin a new term in the four pilot areas: Kensington and Chelsea; Norfolk; Wandsworth and Westminster. The scheme goes national in a year's time.
Around 13,100 eligible parents - 81% of the total - have applied for vouchers and applications are still coming in.
Mr Squire said: 'The start of phase 1 of the new voucher scheme this week is a landmark for nursery education in this country. It marks the first step in our drive to extend parental choice, promote diversity and to raise standards to those of the best. The vouchers that parents of four-year olds have received are a tangible sign that our commitment to quality nursery education.
'This week's start keeps us firmly on course for introduction of the scheme nationally next year. We shall press on until a full year of good quality education is available for every four year old child. I congratulate the staff, governors, parents, local authority members and officials, and many others who have contributed to this week's excellent start, and look to them to keep up the good work.'