Maxalt,
Had exactly the same experience the other day. First time ever in UK airspace I was refused clearance for avoiding action. It was coming down on the Willo arrival from the North with the usual line of TS emanating from the SAM area. Our original track was just about clear of weather but we were then given a heading. When we asked for left or right 10 degrees this was refused. I am 100% certain that the controller was doing as much as he physically could, but I can only assume that not enough restrictions had been put on flow rates to deal with the poor weather.