LONDON—Britain will repay a chunk of old debt. Really old debt, some of which was used to finance World War I.

That bit, along with other scraps incurred as far back as the Crimean War and the collapse of the South Sea Company were bundled together in 1927 into a 4% callable, perpetual note. For nearly a century, it was a good deal for the government. But after rates tumbled this year, that is no longer the case.

The...