Failing that swing by the Avis desk pick up the keys but then 'forget' to drive the car out of the garage until the next morning after you've gone to your hotel .. I'm sure that would work provided it wasn't a location that required a shuttle bus to go and collect the keys [ and I'm fairly sure Madrid is fine for this .. don't think I've rented from Avis there, but with other companies in my experience you get the keys from the desk in the terminal and the cars are located in the multi storey car park over the road ] ...

However as others have noticed give Avis a call first and I imagine it probably can be sorted easily ... trying to do it on BA.com is unlikely to be fruitful