A good article in CCW this week about FBHVC survey into peoples understanding of tyre age. A 1/3rd of classic car owner don't know how old their tyres are
This is a bit worrying when the tyres are the things that connect you to the road and hopefully keep you on the sraight and narrow.
Tyres have a date code - 1st introduced in 1980s - 3 digits - and replace with 4 digits in 2000.
The article attached gives you explanation of where to find the code and how to interpreted it - digit 1 & 2 week of manufacture 3 & 4 year i.e. 08 = 2008 . IF you only have a 3 digit code your tyres are at least 18 yrs old so I would think seriously about replacement
There is no legal age limit but as the article says the rubber hardens and the braking distances increase - worst case the internal walls start to break up (which you dont see!) and you can get a blow out.
Their benchmark of 10 years old would seem reasonable for road use - old should be perhaps ditched or kept for static shows etc.