For 4 and 5 year olds...
Independent schools (fee paying) are called prep schools, or pre-prep. Technically, the age is pre-prep, but many prep schools have pre-prep departments.
In the maintained sector (non fee paying). it would be an infant school (catering for children from 4 - 7) or a primary school (4 - 11). A junior school caters from 7 - 11 year olds, so the natural progression from an infant school.
All schools have a Religious Education lessons and, unless it's a private school specifically providing education for non-Christians, there will be regular assemblies (3 or 4 times a week) of a "broadly Christian nature". Some schools are affiliated with the local Church of England church, but there is often not much difference between these and non-church aided schools (the vicar will be on the governing body and there may be school events in the church - for example, a carol service or harvest thanksgiving). In Roman Catholic schools (still in the maintained sector), there will be some catechism and mass.