The answer is ... its complicated. The BBC is responsible for the collection of the license fee, not the government. There are laws making it illegal to watch live TV without a license but it is enforced by the BBC who prosecute license evaders through the courts. The BBC is a separate entity controlled by the BBC Trust and the Board of Governors and is in no way controlled by or a branch of the government.
Obviously you could argue about political interference but that is just as true with e.g. banks where they can be persuaded by the threat of changes in laws or regulations.
tl:dr - the answer is mostly the BBC