Also, I have always been impressed by how well those in countries where English is not a primary language can speak English.
Am I correct in thinking that mainland Europeans are much more likely to speak English than those in other parts of the world?
Yes and no. Keep in mind that for obvious reasons people on Atlas will speak English pretty well.
Also I think it depends on which part of the world you think of. I am pretty sure that India or parts of Africa have an English fluency that is on par or even slightly better than the average European, although I am never quite sure if English there is a lingua franca, a second language or a first language.
Similarly it also depends on which part of Europe you look at. The Netherlands has an insane English fluency rate, basically everyone can speak it reasonably well there. Meanwhile much of Eastern or Southern Europe has much poorer English literacy rates.
This is self-reported data but it should give a rough idea of English fluency in Europe (even if it is likely to be overestimating slightly):
Very interesting! And it fits with my impressions when travelling Europe.
As you Spanish yourself, do you have any theories on why Spain (and Portugal) score so low?