Hi - these are pretty common in the UK, usually in a natural finish, but otherwise apparently identical. Here's one that recently sold on Ebay:
http://cgi.ebay.co.uk/Kay-Electric-Guit ... 0469578335
As you can see from the label on the back, these are made in Taiwan & the model number's K-32.
I think these were made in the mid-70s & are probably the first "copy era" Kay guitars. The neck construction's interesting, it's the same sort of mahogany ply that was common on early Japanese guitars.
I've actually owned two examples of the bass version of this - a Precision copy called the KB-24. Very heavy, incredibly solidly built (if not exactly well-made), and surprisingly authentic-sounding:
Do you know what the body of yours is made from? All the Strats I've seen have been sandwich-construction solid timber (possibly mahogany), as were both of my basses. The large black oversprays on the contours of your guitar are common on ply bodies, to hide the laminations.
I think these Taiwanese guitars are a sort of mid-point between the Teisco-esque budget Kay imports, and the late 70s / early 80s Korean-made Kays. These were made by Cort and some of the through-neck original designs were very impressive.
Jon.