You can buy the ticket on-line from the airline you travel with.
I found Easy Jet and Ryan Air to be relatively cheap compared to what I am used to at home. They offer flights from Gatwick and Stansted respectively to Biarritz.
Ryan Air and Easy Jet both provide service from Santiago to London.
You will have to do your own cost analysis to determine if it is cheaper to buy two single fares, an open jaw ticket, or return from Biarritz. There are lots of variables in prices depending on your dates of travel and when you buy tickets. Remember there is a cost to get from Santiago to Biarritz (Renfe train to Hendaye, and Transports64 bus to Biarritz airport)
See destination information on airport sites to selects ports of travel and airlines.
Biarritz Airport
http://en.biarritz.aeroport.fr/
Santiago (Labacolla) Airport
http://www.aena.es/csee/Satellite/Aeropuerto-Santiago/es/
Renfe
http://www.renfe.com/
Transports64
http://www.transports64.fr/transports-64?lang=fr