This depends, of course, on your definition of democracy.
The British system is quite democratic in terms of elections. Essentially all adults are eligible to vote and the elections are free and fair.
You can argue that Britian is less democratic than the US, for example, because of its parliamentary system. A parliamentary system has fewer checks and balances than a presidential system like the US has. This means it is more likely to be able to take away the rights of the people.
There are also specific ways in which you can say Britain is not so democratic. For example, it is very easy to sue someone for libel in Britain. This means they have less freedom of the press than there is in the US. In addition, it is easier to suppress unpopular groups in Britain. Their government is currently in the process of trying to prevent a Muslim group from holding demonstrations on the road where the bodies of dead British soldiers are brought when they are returned from Afghanistan.
But overall, Britain is a very democratic society -- they are ranked as "free" by Freedom House and are given the highest possible rating within each category that Freedom House studies.
Britain, which is officially called a United kingdom of Great Britain and Northern Ireland, has a highly democratic country although theoretically the country is headed by a monarchy. The functions of monarch of UK are tightly controlled by the constitution of the country, who does not enjoy any real power for governing the country. The Monarch always acts on the advice of the elected government.
The country is actually run by a group of democratically elected representative who form its parliament. The parliament collectively makes the laws for the country and collectively controls the functioning of entire government executive machinery. Heading the executive machinery is a cabinet of ministers drawn from among the members of parliament. The cabinet is Headed by Prime Minister who is the head of government.