So far I've spoken to:
LAN at the airport: they said go to the office in Lima
BA on the phone: LAN issues, we just sold you the ticket, nothing to do with us
LAN on the phone: we can't refund you anything, talk to BA, they sold you the ticket. Oh, and we won't confirm in writing to BA that the tax should be refunded either

I'm going to try the Lima LAN office later. Failing that I guess I have to escalate within BA. How would I do that?