Do you know where in Wales your mother was evacuated to and where in London she came from? That may help nail down the timeframe and pinpoint the family that you are looking for. I just came across this information at
http://llandeilo.org/catholic3.php.
The Second World War witnessed a significant increase in the Catholic population of Llandeilo. In June 1940 staff and pupils from Coloma Convent School Croydon were evacuated to Llandeilo. A local paper announced their arrival.
"The evacuees arrived on Sunday at 6.40 p.m. They numbered above 200, and the arrangements were carried without a hitch. They were taken from the station to the County School for tea and medical examination. The evacuees included a superior lot of girls who were in the Secondary Schools of the London County Council. They were accompanied by their teachers and sisters of the R.C. The children from Bootle are expected on Thursday".
Sister Mary Clare, one of the sisters involved has recalled her time in this area. Her account is reproduced here:
"In August 1939 about 500 pupils with approximately 20 staff including the Head Mistress, Mother Winifride and four Sisters evacuated their school Coloma, Croydon and set out, for what was then an unknown destination.
All wore labels and carried gas masks. Tearful parents watched the exodus, as well as those left behind for whom other plans were made.
The unknown destination proved to be Eastbourne but six months later danger loomed from across the Channel and once more there was an exodus this time, to a little known town called Llandeilo in South Wales, about fifteen miles from Carmarthen.
There is also a diary written by Mrs M Dineen that can be found at the Imperial War Museum
Ms diary in 4 volumes covering her experiences as an LCC (London County Council) helper with a group of Streatham schoolchildren (one of them her son) during their evacuation to Eastbourne, September 1939 - June 1940 and Llansadwin, South Wales, June 1940 - May 1945 with useful details of her life as an evacuee, her welfare work and involvement with fundraising activities and salvage operations, her billets, rationing and civilian conditions generally as a well as references to war news, Welsh customs, contact with locally based American forces, her strong religious convictions and thoughts on being separated from her husband, a London ARP Warden; also a photograph album and various loose prints, postcards and presscuttings associated with her two periods of evacuation.
My guess would be that the timeframe that you will be looking for is the second half of 1940.
Regards
Mark