For a short time, the British were bemused. Remember that France and Britain were still at odds with each other, France recently supported the American Revolution to punish Britain and now Britain saw that the French were being punished themselves.
Even then there was small support in Britain for the Revolution with a few clubs openly favoring the Revolution in France while keeping quiet about the same idea in Britain. These individuals would tip toe a line that would show their Francophilia in order to not seem Revolutionary to Britain.
However it would change when Louis XVI was executed. The mild bemusement would turn to outright anger at the death of a fellow Monarch. The anger would be predicted by David Hume in his writings on the French Revolution which he predicted would eat it's children.
Some within Britain supported the Revolution out of idealism and Francophilia, others did it out of spite, but when Louis died, Britain would be at war.