Today I learned that 1-1-8 is one of the oldest football formations. It was widespread in 19th century. Why this unusual formation was so popular?
When you say 19th century, you probably mean after 1863, when association football and rugby football split up, The FA was formed and later ball handling, shin-kicking, tripping and holding an opponent were disallowed.
In FIFA article History of Football - The Global Growth, these extreme formations are explained with the fact that despite splitting up with rugby football and change of rules, the game tactics were still similar.
When Scotland played England in Glasgow on 30 November 1872, [...] Both teams employed what might today be considered rather attacking formations - Scotland (2-2-6), England (1-1-8) - but back then the game still retained many of the mob-football characteristics of kicking and rushing and, in tactics at least, probably more closely resembled modern-day rugby than football.
The poster from that match. Source: The FA