The Use of the Modal Verb "Would" in a Certain Passage

Please consider the following passage from my English textbook:

...The commander of the troops called on his men to gather together on deck in proper drill order...Meanwhile, the lifeboats had been lowered. When all the women and children had filled the boats, there would be room for only a very few others.

This is a passage from the reading-text Birkenhead Drill. The lifeboats could only carry one hundred and eighty passengers in total, and there were one hundred, and seventy women and children. Hence, there was room for ten more passengers only.

I'm confused as to the sense in which would has been used in the passage, I have written that in bold. I consulted my Little Oxford English Dictionary to see the use of would, and it describes it thus:

would (modal verb) - expressing an opinion or assumption.

Can we use 'might have been' in place of 'would be'? I have read that structures such as might/may/could + perfect infinitive are used to express something that we are not sure about in relation to the past. I have also read that we use modals would, could for a hypothesis about the future. However, the assumption "..there would be room for only a very few others." is related to the past. So why has 'would' been used here?

Solution 1:

This use of would expresses in the past what will expresses in the present. It is typically used to report the past words or thoughts of someone in a story. In your example, the narrator would have said or thought at the time ‘there will be room for only a very few others’. Because the event as related is in the past, will be becomes would be. In contexts like this, would acts as the past tense of will.