Brazil...
I agree with the comment made regarding direct flights to Brazil, not a hope in Hell.
However, as a frequent traveller to Brazil and flying out of Birmingham, I have always been surprised how many people do fly to Rio. I always ask on checking in and invariably there are four - five who will transit via Amsterdam on the 0600 flight and possibly others bound for Sao Paulo. Add to this, those who may choose to transit via Paris and Frankfurt and the figure grows.
Tangentially there are also those who will transit in Amsterdam, Paris and Frankfurt to countries in Africa.
Given South America and parts of Africa have very strong links with Portugal through language and history I remain surprised that TAP have never developed a Lisbon link from BHX. For me, TAP would be the preferred airline to Rio as the flight itself is shorter than either Paris, Amsterdam or Frankfurt.
TAP could be missing out here, I live in the hope that both they and Lisbon will appear before too long.