If you don't mind changing planes, you may want to consider flying to Iquique (IQQ), Iquique Chile via London on British Air.
Go ahead and book your flight to Iquique NOW!
In order to get the lowest available airfare, book your flight to Iquique as early as possible, since the cheapest seats are booked months before departure. If you are flexible depart on the first Tuesday of the month, as there are usually some great deals and discount airline tickets on offer.