Orson, jigjag
I mostly agree about no upper case for 'the...' but I would make an exception for 'The Times' because it is what appears on its front page and it thus distinguishes itself from the many other newspapers which have 'Times' in their names.
I can also make a case for 'The Derby' as it is such an iconic race. But then how far do I go? 'The Grand National' (yes), 'The 2000 Guineas' (probably not). I'm getting in a mess!
I've heard a London football club being called the Arsenal, but no big T for me there.