There is much more to South America than I think many people in the UK realise. I recently went to Chile and Argentina and many people were rather surprised that we considered it as a holiday destination. When you get there you find vibrant communities and business opportunites as well as sights, wine, flora, fauna and everthing from desert to mountains to rainforest.
If you look at BA they only serve Sao Paulo, Rio and Buenos Aires and then assume they can funnel the rest of the traffic from the UK via Madrid on Iberia. That to me says eveything about the attitude of the UK to South America.
In the aviation community I suspect we're more aware of Brazil, at least, because of Embraer.
THY is indeed trying to build a hub in Istanbul. I get the impression they want to try and emulate the success of the Gulf airlines and, as you say, build on their niche into the 'stans. If you want to get from South America to South East Asia (or vv) Istanbul could well be a valid route as well.
So I take the view why does UK PLC seem to ignore South America?
Apologies, it's a hobby horse of mine!