We would all like the airframes under cover, but history has shown that for medium term 10-20 years, storage outside if properly looked after is not a big issue.
The guardians of the BA aircraft all have great teams working on the aircraft, and with the knowledge from DAS who have been looking after 01 for 25 years, everyone is wise to the issues and not one person looking after an aircraft will allow it to deteriorate.
In Defence of the chaps at Filton, prior booking is required as the exhibit is simply that popular. the 30M figure is based on a full heritage centre, so to get Concorde undercover is a fraction of that amount. The revenue streams coming from the attraction will allow the aircraft to be eventually moved inside. The aircraft is actually under official guardianship to Airbus - UK, who have the facilities and resources to look after it.
G-BOAB at LHR is washed every 2 months. and regularly checked by engineering staff. it is planned for a full check on her to be carried out in a hangar before the winter, she was painted before she went on display.