It has just been announced that flights can now be booked between London City airport and Brive/Souillac airport from the 25th June 2010 from 59€.
Here is the link to the report from La Depeche (French news article) http://www.ladepeche.fr/article/2010/04/15/817208-Aeroport-Brive-Souillac-des-vols-vers-Londres.html
Here is the link to City Jet for bookings!!! http://www.cityjet.com/
Brive/Souillac airport is only 20 mins from Souillac!!!!!!!!!!!