Answer:
"…those children who arrived in Britain to escape Nazi persecution would continue to be supported."
Step-by-step explanation:
The excerpt given in the question talks of the many hurdles and things needed to be done by the RCM (Refugee Children's Movement). It also talks of how even after the end of the war, the needs and safety of the many children who came as refugees be taken care of. Their needs did not end even after the war or the end of the war. The work to get them adopted, safely settled and provide a possibility of future to them remains the need of the hour too.
The use of the words "would continue" in the sentence seems to best suggest that the children's needs did not stop with the war. The efforts to get them stable and established, and safe is of utmost requirement to the movement. Rather than end, it only is the start. The start of getting them a new life, a new safe haven and a new approach of living.