What was the extent of support for radicalism in Britain during the period of the French Revolution and the Napoleonic Wars?

The history of England tended to be marked by compromise, meaning that although radicalism existed in late eighteenth-century and early-nineteenth century England, it resulted in Reform rather than revolution. Part of the reason for this is that some of the reforms enacted in the constitutional settlement of 1689 had already balanced the interests of the people, represented in the House of Commons, with the aristocracy, represented by the House of Lords and the monarchy. In this period, England had a constitutional monarchy unlike the absolute monarchy of France. Nonetheless, many radicals were urging additional reforms on a wide range of issues.
First, the Industrial Revolution was more disruptive in England than in France, because England industrialized earlier and faster. This resulted in the Luddite movement, a group of radicalized workers who destroyed the machinery they considered responsible for job losses.
Next, both Roman Catholics and Dissenters (people not members of the official Church of England) were protesting restrictions on religious freedom and urging repeal of the Test and Corporation acts. These were repealed by Parliament in the nineteenth century. Civil unrest in Ireland remained a constant issue, and many of the Irish Roman Catholics supported the French Revolution and the French cause in the Napoleonic Wars.
Although many in England had been calling for Reform in the 18th century, the example of the French Revolution temporarily muted such calls, but after the capture of Napoleon, the Reform movement regained its momentum The main issue at stake was what might be called a democratic deficit, such as property and gender restrictions on voting and the existence of "rotten boroughs". There was widespread rioting in support of Reform, and thus many politicians argued that moderate Reform would prevent England going the way of France and enduring a revolution. The first Reform Bill was passed in 1832, and subsequent bills gradually widened the franchise.
Although the Westminster Radicals were a small minority, on many issues they made common cause with the Whigs, who dominated Parliament in much of the eighteenth century and regularly alternated power with the Tories in the nineteenth century.