Reddit reviews Britons: Forging the Nation 1707-1837

>How does John Wilkes factor into the British radicalism of the late 18th century?

He doesn't is the short answer. Wilkes was very much an opportunist who used political agitation to achieve his short term goals. Frank O'Gorman argues in The Long Eighteenth Century: British Political and Social History 1688-1832 that, whilst Wilkes was the first 'popular' political figure who "appealed directly to the mass of the people", his focus on 'English liberties' and the patriotic nature of his writings and songs sung at Wilkite events meant that "the Wilkite movement was patriotic, loyalist, even conservative in its ideological stance". However, the Wilkite movement was responsible for constructing a radical tradition in England and popularising a radical view of the Glorious Revolution, though O'Gorman stresses that these were "indirect aspects of the Wilkite phenomenon". Similarly, at the height of the Wilkite movement a dozen radical MPs were elected to Parliament in 1774 and radicals established themselves as a permanent opposition to traditional authorities in London, though they were less successful elsewhere.

So in a way, Wilkes was the founding father of English radicalism in the Eighteenth century. I refer to Wilkite radicalism as English due to Wilkes' staunch anti-Scottish sentiments. However, rather than continuing to support the political organisations he set up, Wilkes lost interest when they no long served his purposes. Linda Colley states in Britons: Forging the Nation 1707-1837 that the slogan 'Wilkes and Liberty' became "expressive of triumph, celebration and relief, rather than a war-cry stimulating further protest". The patriotic and conservative elements of the Wilkite movement made him "too easy to incorporate into a conventional, approving English patriotism", effectively damaging his credentials as a radical figurehead. This is, according to Colley, "one reason why neither the man nor the slogan [Wilkes and Liberty] was much referred to by subsequent generations of radicals".

So, to summarise, Wilkes was essentially a product of his time, a demagogue who could play to the crowd and espoused populist resistance to the established order to gain popularity with a British population hit hard by the economic decline and rise in unemployment after the Seven Years War. Wilkes made the most of the political crisis caused by the accession of George III but had no interests in radical politics beyond his own. As a consequence, although he was significant in its formations, Wilkes left little lasting legacy to the generation of radicals at the time of the French Revolution.

This got pretty long. I was going to deal with your other question about Whig politics but I will leave it here so this doesn't become a solid wall of text.

If you want to really punish/enlighten yourself, here's a decent chunk of the texts from the course list:

Nations and Nationalism (New Perspectives on the Past)

The Construction of Nationhood: Ethnicity, Religion and Nationalism (Wiles Lectures, 1996.)

The Brothertown Nation of Indians: Land Ownership and Nationalism in Early America, 1740-1840

Gendered Nations: Nationalisms and Gender Order in the Long Nineteenth Century

Building Europe: The Cultural Politics of European Integration

Britons: Forging the Nation 1707-1837; Revised Edition

The Clash of Civilizations and the Remaking of World Order

Imagined Communities: Reflections on the Origin and Spread of Nationalism (New Edition)

Globalisms: The Great Ideological Struggle of the Twenty-first Century (Globalization)