Having thought over it some more, here's my take:
- Most popular protest during the period was conservative, e.g. the "moral economy" food riots and the persecution of religious minorities (the Gordon Riots). The one genuine radical movement, the Painite radicals of the 1790s and 1800s were a marginal group with little popular support. The one notable occasion where a radical protest succeeded in achieving change and gained mass support was the Wilkes Affair, which included:
1) A charismatic figure who embodies a particular ideology (in this case Wilkes and Liberty)
2) A popular issue which metropolitan radicals and moderate country-gentlemen can unite on (civil liberties, Bute's abuse of the constitution through secret influence)
3) Support from the London and provincial press, thereby turning Wilkes' cause into a national movement
4) Poor economic conditions/bad harvests contributing to political malaise
5) Symbolism which ordinary people can easily understand
6) An exaggerated government response to an imagined threat of insurrection, which simply fueled further protest.
- Wilkes was a constitutionalist who was arguing that Parliament had abused the constitution. It would be very difficult to see a situation in which a revolutionary movement could be successful. But if may be possible if the following occurs:
1) An extremely severe economic crisis and political malaise (unpopular Ministry and King, Britain at war etc), but the political elite isn't able to claim the mantle of patriotism like the post-French Revolution political climate OTL.
2) A charismatic constitutionalist radical appeals against the government on an unpopular issue (perhaps opposition to the militia in the time of an unpopular war, which would gain support amongst both cosmopolitian metropolitan radicals and the country gentry). He utilises patriotic rhetoric against the government.
3) The radical oversteps the mark and is accused by the government of sedition/treason. A court case takes place, and the press and the country rally behind him.
4) Widespread economic and social disorder, and the army is deployed to restore order but mutinies (the navy did actually mutiny in 1797, the closest Britain got to a revolutionary situation in the 1790s)
5) Parliament unwisely rejects conciliation on unpopular issues such as conscription. The Whig opposition is too small, marginalised and unpopular to carry the baton of reform.
6) Radicals seize the initiative and form an anti-Parliament (was a common idea amongst radicals from the 1770s to the 1840s), claiming to represent "the people" and based on universal manhood suffrage or at least a radical extension of the franchise.
Then:
7a) The monarch and Parliament compromise with the radicals, leading to a constitutional reform bill in which the franchise is radically extended and seats are redistributed. (Something like thre 1867 Reform Act)
7b) The monarch and Parliament unwisely decide to shut the Anti-Parliament down, leading to a popular uprising in London, the defeat of the army and the establishment of the Anti-Parliament as the new government of Britain. Perhaps the monarch is forced to abdicate in favour of his heir, or the monarchy is abolished altogether.
7c) The Anti-Parliament radicals bicker amongst themselves, whilst the monarchy and Parliament eventually restore order and paint the Anti-Parliament as a revolutionary and/or foreign conspiracy. Parliament eventually wins out.
