"That on becoming a British citizen I will be faithful and bear true allegiance to Her Majesty Queen Elizabeth the Second, her heirs and successors according to law.
"I will give my loyalty to the United Kingdom and respect its rights and freedoms. I will uphold its democratic values. I will observe its laws faithfully and fulfil my duties and obligations as a British citizen."
This "oath" is contradictory, asking those who take it to "uphold" democratic "values" while pledging allegiance to the monarchy. And what does it mean to swear "loyalty to the United Kingdom"? Does that mean the decisions of the state? What happens if laws of the government violate "its democratic values"? Which takes precedent, observing "its laws faithfully" or upholding "its democratic values"? Given that the oath takes have to "fulfil [their] duties and obligations as a British citizen" and "be faithful and bear true allegiance" to the monarch, it seems that obeying the state is more important that upholding "democratic values" (particularly as this oath shows contempt for such things).
This is not to mention the fact that there are tens of thousands, if not more, of British people who would refuse to take this oath of allegiance. After all, it is based on the premise that we are all subjects of the monarchy and not citizens (even if it uses the word). It also assumes we live in a "democratic" country, yet by any sensible definition of that word that is not the case. Increasing the extent and scope of our "democratic values" almost always involves coming into conflict with the state which claims to govern the "United Kingdom" and ensure the laws it passes are enforced. And how "democratic" is a state whose government happily ignores the will of the people and lies to it in order to invade other countries? Or that the fate of millions of people are decided by 600-odd people, under the pressure of the state bureaucracy and big business?
Ultimately, in a democracy the assumption should be that as citizens in a democratic society "loyalty to the United Kingdom" may or may not be forthcoming depending on the legitimacy of the states' activities. Moreover, libertarians are that the important struggle in society is between subjects and states, workers and bosses, to increase freedom and "democratic values" by eliminating concentrations of power. How can you "uphold democratic values" by pledging allegiance a system which systematically disempowers the many in favour of a few?