I think this extract from the Wikipedia article (mentioned by Gadget) on the British Liberal Party may help to explain:
The Liberal Party was one of the two major political parties in the United Kingdom, along with the Conservative Party, in the 19th and early 20th centuries. Beginning as an alliance of Whigs, free trade–supporting Peelites and reformist Radicals in the 1850s, by the end of the 19th century it had formed four governments under William Gladstone. Despite being divided over the issue of Irish Home Rule, the party returned to government in 1905 and won a landslide victory in the 1906 general election.
While there was a socialist faction (the Labour Party) in British politics in the 1920s, I think the distinction here is less about right wing or left wing beliefs (as we understand them today), and more about the kind of liberal politics that your great grandfather may have espoused. Early twentieth century liberals (including the Liberal party itself) were quite disunited about what they stood for. Many were interested in socio-economic reform and welfare issues, (in contrast to the Labour Party which was more focussed on trade union and employment rights, in addition to economic reforms), while others were more concerned about extending the franchise (the women's suffrage movement in particular but also wider political reform such as republicanism), while others again were more focussed on Britain's role in the world: being pro free trade and anti-war etc.
The term radical being applied to your great grandfather suggests he was perhaps more entrenched in his views and would have held strong opinions on subjects such as republicanism, modernism, secular humanism, anti-militarism, civic nationalism, abolition of titles, rationalism, secularism, redistribution of property, and freedom of the press. All of that chimes well with Welsh politics of that time.
So to summarise, he was probably fairly left wing, possibly less concerned about the specific issues around workers' rights, and more in favour of social reform more generally.
