Based on joint service of KLM / Air France or Iberia you may consider to book attractive return flights from Europe to Lima, capital of South American Peru. Cheap return flights from main airports in UK or Benelux to Lima are now starting at £436 or €521. On your way you would have to accept additional layover either in Panama or Bogota (in most of cases). On the other hand you may visit Peru for a reasonable fare also without need of routing via US which is usually the cheapest option..
In case of interested in this KLM / Air France promotional sale please look for flights in travel period between 1st of September till 3rd of December 2015 and in January till end of February 2016. (Based on date of your outbound flight to South America). We have managed to find the cheapest flights mainly within January and February 2016. Look for flights departing from cities such as Manchester, London, Newcastle, Birmingham, Edinburgh in UK or Brussels. Please refer to below booking samples to Lima if interested in this deal.
Booking samples
Brussels - Peru from €521 (based on Iberia, travel dates in April or May 2016)
All these European cities are well connected by many low cost airlines. To make a basic idea how to reach them from your hometown you may use service of Skyscanner.
Booking sample of cheap return flights from UK or Benelux to Peru from £436/€521 here. In this case you would be flying from Manchester to Lima on 24th of January 2016. Your return flight from South America to UK would take place on 12th of February 2016.