Whilst the philosophical views posted here are very worthy (and essentially this comment is irrelevant if you're on a fully flexible ticket/aren't pushed for time), if you get stuck on the outer reaches of the Piccadilly line on the way back to the airport (and a 'body under the train' or kids running on the line is probably as likely as a security alert), don't expect to just be able to walk onto the street and flag down a passing taxi.

It could work out as a very expensive stopover indeed...