Difficult to say.. I must have built most of Airfix Series 1 kit at one time or another, and some of those are indeed old! My first ever kit was Airfix Me-109G, in its blister pack, costing at the time some 20 Belgian Francs (that would be 50 US cents in today's money). That was in 1974... Gosh I'm going to hit 30 years of continuous scale modeling next year!
I also remember building some Frog, Hawk, Glencoe, Lindberg and Revell kits that must have been designed years before I was even born.. In my loft, I have Lindberg's XB-70, a kit designed in 1963, although my 'copy' is of the re-release of '69. That's possibly the oldest kit I have now to build. As far as completed models, that I still have around, then it would have to be Airfix's Mk I WWI tank, probably from the '60s (and still a great looking model!)...