The publisher might have retained copies of the reviews. Unfortunately, Longman, Green & Co seems to have been subsumed into Pearson Education (which includes the Longman Imprint). It might still be worth contacting them:
Pearson Education
Edinburgh Gate,
Harlow, Essex,
CM20 2JE,
United Kingdom
Tel: 01279 623623
Alternatively, you might well find a review by browsing through 1953 copies of the Times Literary Supplement. Your county reference library might have these available on microfiche. Otherwise, you'll need to contact British Library Newspapers at Colindale. Contact details are here:
http://www.bl.uk/about/locations.html
The British Library will probably be able to suggest other journals which might carry reviews of E.M.Challon's work. (I wonder why she thought it necessary to use a pseudonym when she wrote 'The Charioteer'?).
Chris