One of the best books on the Home Front in WW2 is "The People's War" by Angus Calder, which you should be able to get from your library. The first part of Chapter 2 is the bit you need.
Some important points:
1. Government/officials believed British cities would be heavily raided as soon as the war started, so needed to evacuate quickly;
2. Not only children, but also mothers with babies and toddlers, and pregnant women, were evacuated;
3. Many families made private arrangements (for example if they had a relation who lived in the country)
4. Many people in the "reception" areas were appalled at the state of some of the children billeted on them; it was the first time they had encountered people who lived in desperate poverty.
5. When the expected air raids did not happen, many evacuees went home again.
Hope this helps.