Figures on the number and proportion of children eligible for free school meals are published, for all local authorities in England, annually. The figures can be found in the statistical first releases available at: https://www.gov.uk/government/collections/statistics-school-and-pupil-numbers
For each year, the figures for the local authority of York, and for England, are shown in local authority tables 8a – 8d.
A UK figure is not available. As education is a devolved matter, statistics on schools are published separately by the four administrations.