Can anyone tell me what the approx 8 inch long, 8mm rubber hose that comes out of the no3 cylinder just below the carb intake rubber is? Is it a breather and where if anywhere does it go. Was disconnected on my bike when I got it and not sure if it needs to connect anywhere or simply hang loose. Can post a pic later if the description doesnt ring any bells!

That is the vaccum hose which connects to the fuel tank if its not connected and your bike is running ok then someone has done the HRC fuel tap mod to your bike which isnt anything to worry about just turn of fuel every time your finished with bike and check fuel tap for leaks now and again
The breather hose is the one which comes up and plugs into the top of the tank at the front

+1

Should be connected to the smaller spigot on the outside of the fuel tap.

I'd be thinking to refit it and make sure the diaphragm in the tap works. Does your bike pee fuel out the tap when turned to on?

cheers guys, the bikes in bits and in process of going back together will have a look on the tank to see where it connects. Only pipe that was connected when I got the bike was the fuel feed pipe. Bike certainly started and ran but hesitated when revived.. Never ridden the thing YET!!!