Pickety explains this rather well in Capitalism in the 21st Century.

During the 19th century, inflation was more or less non-existant and interrests where stable at around 4%. During this period, most investors sought a stable haven for their money with little expactations to actually cash out the original investment (unless something unforseen happened), meaning that all a country as UK needed in order to service a debt at 200 % was the capacity to pay about 8% of GDP every year in interrest.

Modern financial systems are much more complex with varying inflation, interrest and a lot more alternatives for investors to deposit their money, which means that "runs" are much more likely.

However, it should be noticed that the US on a global scale still works in a way similar to what national governments did during the 19th century, as a safe haven for investors.

Japan's Debt to GDP is 214-234% depending upon who you ask. So it's not unthinkable.

Source: CIA World Fact Book/IMF

Systems of national accounts (GDP) were only developed in the 1930s and only became seen as the most important economic indicator after WWII. So nobody in the early 19th century knew what the debt to GDP ratio was, let alone whether or not it was too high.

Also, at that time government expenditure counted for a far smaller part of the overall economy, the bulk of it going towards the armed forces. This means that the government had a lot more leeway to raise revenue to pay for debt without causing the kind of disruption that fiscal austerity causes today. In fact, income tax was first introduced in the UK during the French revolutionary/Napoleonic wars.