With a potentially perilous exit from the European Union looming, many Britons face a squeeze on living standards, but for one group, it may prove particularly tough.

Without changes, younger Britons risk becoming less prosperous than their parents’ generation for the first time since the Black Death pandemic that ravaged the region in the Middle Ages, according to the country’s chancellor of the Exchequer, Philip Hammond, who delivered his annual budget on Wednesday.

That danger could also prove critical for Mr. Hammond’s Conservative Party. The divide between generations, long debated in Britain, became a newly urgent topic for the Conservatives after a general election in June, in which they unexpectedly lost their majority in Parliament. Young voters turned out in force for the opposition Labour Party, led by the left-wing Jeremy Corbyn.

Mr. Hammond’s announcements on Wednesday focused on housing, seen as a major factor in Britain’s intergenerational divide. Older, asset-rich Britons have benefited from rising home prices, while many younger people have found themselves having to pay high rents rather than buy, particularly in London and southeastern England.