There are no central records of children’s evacuation during the Second World War.  If any information has been retained this is likely to be held locally so you could try the archives of the area your relative was evacuated from and to.  You can find the addresses by using www.genuki.org.uk or www.familia.org.uk
 
Useful addresses:

Evacuees Reunion Association (ERA)
The Mill Business Centre
Mill Hill
Gringley-on-the-Hill
Nottinghamshire DN10 4RA
Tel: 01777 816166
Website: http://www.evacuees.ndo.co.uk/

The Research Centre for Evacuee and War Child Studies
Bulmershe Library
University of Reading
Bulmershe Court
Earley
Reading RG1 6HY
Website: http://www.extra.rdg.ac.uk/evacueesarchive/