The United Kingdom and many of the nations of Europe felt threatened by Napoleon essentially challenging the status quo. While maybe not very true, they felt he brought revolutionary fervour and other ideas that challenged the absolute power of many monarchies (Britain wasn't an absolute monarchy though) and he essentially disturbed the power balance in Europe.

Britain was also near impervious to invasion, due to their naval victory at Trafalgar which broke the French fleet under Villeneuve. This was of course a threat.

Keep in mind that there had recently been a war between France and Great Britain, one that dealt a stinging defeat upon the British. Then, a second upstart republic emerges that also overthrows a monarchy, this time in France itself. The British had given in once, they weren't about to again. The French were aggressively expanding (Napoleon inherited the Revolutionary Wars) and to many, it was obvious that the Revolution was a danger to the balance of power in Europe. George III began welcoming shiploads of emigres from France and equipped many of them to fight the French Revolution.

According to Vincent Cronin, the English view of Napoleon Bonaparte grew out of the war and hatred of the Revolution. From the first moment that Napoleon entered the public's eye throughout Europe with his First Italian campaign, Britain at once began to paint a picture of the upstart Corsican Ogre. In Egypt when it came out that Josephine had been adulterous, Napoleon sent heart felt letters expressing his pain back home. However Nelson intercepted them and released them in England, much to Napoleon's embarrassment. Lets just say that from early on, neither liked each other very much. The King called Napoleon 'the Corsican tyrant' and his war party was vehemently outspoken against Napoleon upon his rise to power.

Britain had already suffered a defeat and the loss of a whole lot of money against France in the American Revolution, so why would they want to pursue further war? Napoleon was a hero, he stopped The Terror in France and brought stability. The Revolution, it became clear, wasn't going anywhere so long as Napoleon stood in power, the Bourbons were not going to return with him around. Britain sent at least two assassins to kill the First Consul, which led to him becoming Emperor, to protect himself as a monarch rather 'just a general,' as they saw it. Napoleon executed the Bourbon Duc d'Enghien(at Talleyrand's behest) who was in contact with Britain and in their pay to fight against France.

So when it came to the Treaty of Amiens, both sides viewed each other with great mistrust. In the end both sides felt justified that the other was the responsible for the breach. Britain wasn't going to uphold their end of the treaty because they felt this "Corsican, Jacobin and ambitious conqueror, was not a gentleman and so he could not be trusted."(Cronin) Napoleon asked Britain's diplomat Whitworth why Alexandria and Malta hadn't been evacuated as per the treaty, he replied "I suppose you mean Piedmont and Switzerland..." neither of which are mentioned in the treaty. Napoleon responded "the boundaries of Europe should have been discussed before Amiens, not after."

The British government just didn't like him, didn't trust him and was prepared to fight to stop him. Even though the King and others never liked Napoleon to begin with, they surely didn't like the fact that he was a strong and fearless ruler. He dispatched troops to retake Haiti from the slave revolt (they feared his use of navies), he annexed the Cispaline republic (a republic he set up during his First Italian Campaign) and sent in troops to preserve pro-French rule in the Helvetian Republic, which according to the Treaty of Luneville should have been allowed to be independent.

So, neither side was innocent, and both sides were more than willing to pursue war when it came to it. Britain was taking a hard line after the American Revolution, and Napoleon was a soldier, unafraid to pursue war as 'politics by other means' as Clausewitz would later put it.