My daughter who does not need me to copy edit!
How easy it is to go into edit mode when you read a manuscript. After all, once you fix the English, the science is easier to understand. But then you might start wanting to move paragraphs around and get sucked into the whole structure of the piece.
Don’t do it! Do not succumb to this temptation. All you need to do is to write one sentence. “The English in this piece needs work.” Do not do that work yourself. If the English is so poor you cannot follow the argument, then reject the paper for this reason and do not do anything further.
The truth is, you do not have the time! You are not being paid to be a copy editor. The more ambitious and self-knowing people in your field will have learned this lesson a long time ago. You need to be doing all the other things a busy scientist does: teaching, reading new studies in your field, crafting your own papers and grants, and of course doing the actual research.
You may feel sorry for these poor authors who are trying so hard and just don’t have your advantage of English as a native or well-learned language. This is not your job. They can easily hire people to fix their English. It is the least of the expenditures involved in doing and sharing science.
As with so many other altruistic tasks, this is a pitfall that women more than men fall into. So just remember, if the English is so poor it gets in the way of understanding the paper, reject it and mention this reason. Reviewing should not become onerous because of language.
The only papers I edit for English are those headed to publication from my group or with me as an author. And by the way, I love English. I love language and Grammar. After all, who else just listened to Benjamin Dreyer’s marvelous Dreyer’s English: an utterly correct guide to clarity and style? reviewed by the New Yorker here.
Sociobiology 
Hi Joan, Well, I do exactly as you describe, go into copy editor modus when reviewing (some) manuscripts. It is almost like a nervous tic, practically can’t help myself. But I mainly do this with mss I know are going to get published, that are in my field, and that I want to be readable rather than just understandable. I do explain to the authors a lot of the grammatical errors I am correcting. I don’t know where you got the idea that scientists in poorer countries can afford to hire someone to correct their English: they cannot. I visited an ecologist a few decades ago in El Salvador who I learned raised orchids for sale because his salary is not enough to support him. The times I do not correct English are mss with co-authors that I know or strongly suspect are native speakers–that should be their responsibility, it seems to me.
Great that you do this. You have the time and a secure position. I mostly have in mind young people themselves not with a position yet and needing to get their own work out. I could decide to use my time this way also, but have decided to help in other ways. As to funds for English, I think it is variable and ideally journals would pay for this service.