THAT was fast!
They were incorporated in 1941, and were intended to be the English version of Paris Couture Syndicate. After Paris' occupation it was clear that the centre of fashion was no longer going to be coming from that city (despite Schiaparelli's assertion that even under occupation Paris will never be usurped as the leader of style -- she was a bit of a loud mouth media hog actually...)
Anyway, LaGuardia was REALLY pumping up New York as the new centre of world fashion but Stanley Marcus (of Neiman Marcus) was anti New York and was pumping up Chicago as a possible replacement. Meanwhile California's apparel industry was blossoming and becoming more important with each passing month. The London Society was formed as a way of gathering together Britain's talented designers and make a stab at taking over the head of the class. The problem is that between rationing, austerity they didn't have a shot in hell. The Society was commissioned to launch the utility clothing scheme in 1941 and they provided the basic collection for its launch in spring 1942.
They society was around for a while longer but it seems to have died in the late 1950s or early 1960s, just before England's rennaisance as a world leader in fashion in the mid 1960s with that whole carnaby street youth movement thing beginning with Mary Quant. There was a different organization that developed for the youth designers in the 60s and I suspect it was because they were into hip, chic, fun clothes, while the old standbys of the original London Designer's Society were more Queen mum and tweeds types -- generally speaking.
So, long story short, that is great to get that name but I wonder if perhaps she wasn't involved with them at the start and came in later. At least its a lead. There has to be a write-up on that London Fashion Desaigner group SOMEWHERE.