Fowler's Modern English Usage, Sir Ernest Gowers, ed. (2nd Ed. Oxford 1965) follows the rule that I learned long ago: Capitalize if one is referring to a specific office or holder of an office, even when the name is not used (thus, the person who works in the Oval Office is always the President, not the president), and do not capitalize if one is referring to an office generally. (Thus, "The funeral was attended by presidents and kings.")
In
Fowler's we find: "The use of Capitals is largely governed by personal taste, and my own, while not favouring seventeenth-century excess, happens to favour even less the niggardliness now sometimes apparent. The printed page that is starved of capitals suffers not merely in appearance (to my eye at any rate) but also in function, for denial of capitals to well-known bodies, institutions, officials and the like militates against ready reference."
