I think it's completely different when the mother speaks English in a non-English speaking country- English is a very dominant language, there are tonnes of signs even in different countries in English, pop music in English and so on. Plus it is taught across the world in schools in so many countries. I'm not sure it's such a big deal learning English that way to be honest, millions of people have learned it as a second language (i.e. not from their parents) because of the availability of English/American films, opportunities to speak it and so on. I have family who did English through their mother and they have very heavy accents and seem to be at no advantage to those who learned it at school or later in life, or who just came here and immersed themselves. About 1/6 of our university intake have english as a second language and very few of these have this from their parents.
Now, if the mother was Finnish and was over here with an English partner who didn't speak Finnish, the chances of just learning Finnish through OPOL without great reinforcement/living in the culture/endless insistence is very low. I know probably about 6 couples where the minority language is not spoken by the children, and while they comprehend some of that language, they are far from being able to use it.
I'm not saying this to depress anyone, but the idea you just chat away and the child absorbs it is a little naive. Children also differ in their ability to pick up languages, we have one family friend whose child is simply amazing at picking up languages, and aged 10 speaks 4 very well, we have friends who have children who don't speak the second language despite it being the home language.
Countering the dominance of English is very hard, Spanish is a good language to do this with though, because it's very widely spoken and access to materials/resources/music/countries which speak it is huge (unlike say Finnish!)