The descendants of the Duke of Cambridge did not have succession rights due to his marriage, which was in contravention of the Royal Marriages Act.
Quite true. His wife Sarah Fairbrother was an actress who had bastards by two other men before he met her, then two more bastards of his, and was pregnant with a third child of his when they married. That was in 1847, by which time Vicky and Bert had five children.
While Vicky and Bert are childless, and the Cumberland line (Ernst Augustus and descendants) is excluded, the heir presumptive is the Duke of Sussex, who is 70 and childless. He died in 1843. After him is Adolphus, 1st Duke of Cambridge (died 1850); it was his son George, later the 2nd Duke, who married Sarah. Adolphus has two daughters as well: Augusta (1822) and Mary (1833).
Possible impacts of Victoria's childlessness include George getting his chain yanked. The question is when the lack of children becomes a worry. Sarah got her hooks into George in 1840; their first child was born in 1843. If Cumberland (d. 1851) and his son aren't wanted, then George becomes de facto heir apparent (his father won't want it). The powers-that-be in Britain may tell him to knock it off, buy/scare off Sarah, and marry him to someone respectable.
If George is a lost cause by the time the problem demands a solution, his sisters are potential answers. They both married German princelings, Augusta in 1846 and Mary in 1866.
One thing that might trigger the worries is if Victoria has a difficult first pregnancy ending in stillbirth or miscarriage with complications that either nearly kill her or appear to injure her fertility. That could happen as early as 1840.
The other question is when, if ever, the British considered excluding the Cumberland line. Victoria's accession in 1837 ended the union of crowns with Hanover, and British leaders were nearly all pleased, AIUI. But Ernst Augustus was still heir presumptive until Victoria's first child in 1840. Was anything done or talked of then? Later on it was moot because of Victoria's large brood.
If Victoria still lives until 1901 - Augusta succeeds, aged 79, or passes the succession to her only son, Adolphus (1848-1904). (Though Victoria's very different life will no doubt butterfly Augusta's life.)