Of course ash is subject to gravity, though obviously affected somewhat more by air currents. If, as bradt says, the ash cloud is between FL200 and FL360, and as you've probably noticed by lack of a layer of ash blanketing the country it most likely is concentrated at those levels, and if it's safe for VFR traffic to bimble around outside CAS, then why is it impossible for commercial IFR flights to operate at lower levels???
To say that ash is "subject to gravity" (which it is) in isolation is to ignore whatever you once learned about water vapour on your met course back in the day! Water vapour, more commonly known to us as "cloud", is also subject to gravity. Does it come down? Yes, quite often in the UK. Is it capable of staying up or even rising? Yes it most certainly is! The ash cloud, rather than descending in one large blanket, is likely to dissipate as it gets further from its Icelandic source. Some of it will fall to the ground though in small enough concentrations to be unnoticeable, and some of it will likely stay in the atmosphere for years. Some of it will mix with water vapour and fall as rain or hail. What it is extremely unlikely to do below 20,000 feet or so, is be present in significant concentrations such as to endanger an aircraft.