Final answer:
Bevanism, named after Aneurin Bevan, a British Labour Party politician, was influenced by traditional grassroots Labourism and Liberalism, combining the working-class movement with Enlightenment-rooted ideologies of progress and rationality.
Step-by-step explanation:
Bevanism was influenced by traditional grassroots Labourism and Liberalism. In the context of the early 20th century, numerous political ideologies were in contention. Liberalism, with its roots in the Enlightenment and bolstered by its association with rationality and progress, came into prominence following the Napoleonic Wars. Likewise, Labourism was deeply connected to the working-class movements and aimed for social welfare and collective bargaining for the workers within a parliamentary democracy framework. The combination of grassroots Labourism and elements of liberalism shaped Bevanism, particularly with its moderate social welfare priorities and a focus on egalitarianism within the UK's National Health Service post-WWII.