The UK is a "(democratic) parliamentary constitutional monarchy", which makes it a democracy, but importantly it's still a monarchy as well. Being one thing doesn't necessarily exclude the other, even if one must limit the other.
Most of the time, the laws and bureaucracy in the UK refers to 'The Crown' instead of to the king or queen personally. And ahmedfromtunis expressed surprise that this is not universal (but only 'most of the time').
