BAA existed long before Mrs Thatcher became Prime Minister. As the British Airports Authority it controlled a number of airports around the country including LHR, LGW and STN. As a nationalised 'industry', it was inefficient and monopolistic, but in those days Governments had a much greater say in regulating aviation.
It was privatised by Mrs T, and the shares were owned by mainly UK investors. Prior to its sale, there were calls for it to be broken up, but it survived whole because it was easier and more beneficial to the taxpayer to sell one entity. It was, however, regulated.
When a Spanish company bought it out, they used an enormous amount of debt, and control of a major slice of UK infrastructure moved to Spain.
Obviously, private companies should not be regulated unless necessary, but in this case, a foreign operator was acting monopolistically by cross-subsidising its airports and distorting competition. Any inhibitions to free competition are investigated by the Monopolies Commission, who have powers to protect consumers from such behaviour.
The decision to break up BAA is long overdue, and should be supported.
Thinks... why is there only one monopolies commission??
