Usually towel rails are fixed with this tiny screw onto a bracket hidden behind, which is in turn fixed to the wall. So, one way or another this screw has to be shifted to release the rail. Try a squirt of penetrating spray, apply a bit of heat with a hair dryer maybe, use a good condition screwdriver which has the correct end for the screw (some screws are allen, hexagon headed types).
John, January 2008