What is the origin of the phrase "pilgrims and strangers in the/this world"?

The origin of the phrase goes back almost four thousand years to the time of Abraham. Since then however it has been translated in numerous ways from Hebrew into Greek and Latin and to English, and numerous other languages.

Abraham had no land or country of his own, so when his wife died he had nowhere of his own to bury her. He therefore asked the community he was living among, where he could bury her. He explained that he was a stranger amongst them and that he was a traveller. He did not belong to the community originally, nor did he intend permanently to settle there. He was a stranger and traveller (pilgrim). Thee are many translations of this request, in Genesis chapter 23, verse 4. These include "stranger and sojourner" or "comeling and pilgrim"

Hundreds of years later this same concept was applied to the Jews in Egypt in the time of Moses, they neither felt they belonged in Egypt, nor did they intend to stay there (Exodus 6 4).

Both Hebrews 11 13 and also 1 Peter 2 11 pick up on this. Hebrews is directly referring to Abraham, whereas Peter is using it as a metaphor for the idea that Christians (perhaps all people) do not belong to the world but are just passing through.

For over a thousand years the major version of the Bible used in Western Europe was the Vulgate, written in Latin. The Douay was a translation of this, a translation from Latin into English. This rendered Hebrews 11 13 with the phrase "pilgrims and strangers on the Earth".

Although Bunyan commonly used the King James version and the Geneva version (both of which have strangers and pilgrims) he would have been familiar with the Latin version and its translation into English.

The Franciscan Rule was based on the Latin, so that explains that.

Regrettably the OP cannot quite recall where he came across the phrase, but if it was in Victorian literature, as he suspects, it would most likely have been a character quoting from Pilgrims Progress, which was immensely popular amongst Protestants, or from the Douay Bible translation into English, used by Catholics. Neither the King James Bible nor the epistles appointed in the Prayer Book to be read on the third Sunday after Easter (Hebrews), or on Accession Day (Peter) have "pilgrims and strangers" but all have "strangers and pilgrims"

As it has been translated so many times, the exact wording is perhaps less important than the twin concepts it conveys: we do not belong here, and we won't be staying.