Did children wear corsets in the thirties?

They were invented in 1908.
http://www.contourandcream.co.uk/corsets.htm
Liberty Bodice introduced - this was worn by many children until the 1950s
and
was produced until 1974. The idea for the bodice came from Frederick Cox,
and
his daughter, Freda Cox, became the first model for the marketing
campaign. The
original rubber buttons came from Market Harborough's Harboro' Rubber
Co. -
still a successful industry today.
--

Martin

Live in Harborough, the Rubber company have just sold their old original
premesis and moved, most of its been knocked down apart from the original
listed mill from when it was called Danite Mills.