shins, plenty of youngsters were evacuated to the US during WW2. My MIL was one of them. She never forgot the incredible generosity of the Americans.
There were initial plans for evacuating over 211 000 children overseas, but with the sinking of City of Benares by the Germans, and the death of 70 children, the plans came to a halt; but about 14000 had already left.
MIL was on one of the last ships that left: she always remembered how all the dockers in Liverpool lined the quay and waved and shouted "Goodbye, kiddies, good luck kiddies". They knew what had happened to the last ship. 
As for internal evacuations, it is estimated that almost 3,75 million people were displaced in the UK. So no, the British did not sit around bravely allowing their children to be bombed to smithereens.
In WW1 250 000 Belgian refugees made it to Britain. That is over twice the number of estimated refugees living in the UK at the moment.