No, it shouldn't be under your floor boards. If the radiators have been moved around in the past, it is possible that the radiator that was moved, use to contain the drain cock on one of its tails. When the old position was capped off, the plumber/DIYer obviously forgot to refit the drain cock on another radiator. To get over this initial problem, you'll need to buy union valve tail of the same size, a 15mm olive, compression nut, 6inches of copper pipe & 20mm hose clip. Put some tarpulling under rad, turn both the valves off on the smallest ground floor radiator nearest the door and open the bleed nipple. Put a tupperware bowl under one of the rad's union nuts and loosen until water drops into bowl, tighten when it gets full and empty. It may take sometime, but you'll have to repeat the process until rad is drained. Once drained, get a bigger bowl by the side of you and unscrew both union nuts. As you lift this rad off the wall tilt it straight into the bigger bowl to get rid of the excess. Now comes the clever part. push the olive and compression nut over copper pipe and push the pipe into the threaded union, it won't go in all the way as it was not intended to take copper pipe, it was designed to screw into the rad! Make the compression join to the pipe and attach a hose to the over end with the hose clip. Then connect the union to the valve. Hey presto, a drip free drain cock when you open the rad valve. Whilst the sytems drained, fit a new drain cock - my fingers hurt!
good luck!
Gary
P.S: alternatevely, if you've got more time
than money, You could just bucket the water out straight from the valve!