Initially the British government was quite favourable to the revolution, as were the Opposition and many interested parties outside of Parliament. There was the famous pamphlet war between Edmund Burke, Thomas Paine and Mary Wollstonecraft (among others), and Burke was seen largely as an alarmist minority. But he was proved right, ultimately.
Hostility to the revolution grew after the new French legislature began attacking church and property rights throughout France. The legislature came up with some truly crazy, crank ideas based on metrical assumptions of human nature rather than application based on past experiences. Then the King was executed, the monarchy abolished, and the Terror ensued. Once that happened, British opinion to the revolution turned resolutely sour.
There's some thought that if Napoleon had satisfied himself with the borders of France and refrained from his habit of using war as a first resort, the British might have grudgingly acknowledged him as France's rightful sovereign. But as he was determined to dominated Europe, and it had long remained Britain's policy to prevent one power doing that, Britain could never accept Napoleon on the throne.