I want to fly from GIG to LHR in July during the Brazilian winter school holiday (so pricing is high). I have just run a booking on the BA site for a family of 4 that is coming out to $12,798. If I make a booking from GIG-LHR-MAD, on the same dates and flights, the price comes to $11,051. That is two extra legs (LHR-MAD, MAD-LHR) but a cheaper overall price. What gives? Can I simply choose not to fly to Madrid and stay in London for the two weeks or is that not possible? How would the check-in at LHR work for the return leg given that it is supposed to originate in MAD?