Just solved the problem myself.
Went to Program Files (x86)/Ubisoft/FarCry3/bin and clicked on farcry3.exe
Doing this started Uplay and showed FC3 and I was then asked for my key. Uplay is currently downloading the update.
I did not get asked for my key when I installed the game.
Seems that the installer should have automatically started farcry3.exe but it didn't on my system.
Just disappointed because it seems whenever I buy a new game on PC I have to waste time sorting out some silly installation problem just to get up and running. Fortunately this was an easy problem to fix (ie the first thing I tried worked).