How do I find out how old a house is?

You can do a title search in your local government for the building permits but if all else fails there is a secret.

I you can reasonably assume that the bathroom is original try this. Remove the top from the flush tank on the toilet. Many times there is a manufactured date cast into the mold. It isn't exact but if it is original (that's a big IF) you can get a ballpark figure on when the house was built. If not, it will tell you the approximate date the bathroom was remodeled.

Good luck...

Probably isn't a website, but like others said, in the US we go to the court houses and look up the deeds and trusts on the house.

I am not sure how they do it in the UK, but in the US you can check the records of the home with the County Building where the home is located; they have everything on record from every owner, price paid, etc...