I'm an English teacher living in Germany. I completely disagree with your theory. Most people don't go out of their way to practice a foreign language, which is why they don't get better at it!
The UK attitude to foreign languages is appalling and has many factors but I really think that sadly the biggest barrier is arrogance. You can see it in the OP - this assumption that English is so prevalent and important and universal. It's not. It might be more commonplace, but it's not that much more difficult to find sources of other languages, if you want to find songs, TV programmes, films, books, websites etc in other languages - google is your friend.
We seem to think that because English is "so important and prevalent" that there's not much point learning anything else and that other people will find it so easy to learn English that we might as well not bother. This is just pure laziness, and while it probably doesn't matter for anyone over 30 right now, it damn well is going to matter for our kids, who are going to be hugely short changed and very uncompetitive in a global market if they inherit this unfortunate tendency. (Anyone in between those ages would find learning a second language - any - to be a huge boost in their global competitiveness).
DH always complains that people switch into English and won't speak German with him, but I've seen him, 9/10 he doesn't even try, he just says (in English) "Sorry I don't speak German" or (in stilted German) "Sorry my German's not good". I've had far more success by saying "Please can you speak slowly" - if the subject matter is complex and speed/understanding is important then usually they do switch into English and I don't mind that at all.
It doesn't take that long to get a basic footing in another language but you do have to put the work in and recognise that studying/learning the theory of the language is only about 10% of it, you have got to use it. Languages are skills, not knowledge. Are you going to get better at football by reading about football tactics, or by playing? What about drawing? Can you become a great artist by studying important artistic techniques? Or driving? Should we just scrap the practical test and lessons, theory's enough, right?
You've got to speak it. It's no excuse that "most foreign speakers in the UK speak another language" - so? You don't have to sit around and wait for language speakers to just happen across your doorstep!
Seek them out - according to EU survey in 2006, 23% of the UK population can speak/understand French, 9% can speak/understand German and 8% can speak/understand Spanish. There are meet up groups all over the country for speakers of foreign languages, you can put up ads seeking language exchange (they speak in XXX with you, you speak in English with them), study groups attached to local colleges, libraries or universities which you may or may not need to be a student to join, evening or weekend classes, and if all else fails, it's back to what you're doing right now which is browsing the internet - there are forums in every conceivable language, there are skype groups or discord channels or IRC chat rooms, email groups, you name it. Search "XXX learners" and you'll find them. If you're learning a European language, get yourself on Skyscanner and AirBnB and go for a weekend away, with the goal being to USE language as much as you can. It doesn't matter if your sentences are crude, that's how you start, and the only way you'll get any better. Ban "I don't speak X" or "Sorry my X isn't very good" from your vocabulary! Learn the phrase for "Speak slowly please" instead. IME, most people are absolutely delighted when you make the effort to understand and/or try to make yourself understood. And if not? Oh well. Perhaps they were having a bad day.
Don't rely on the UK's school language learning because it's crap. It's all theoretical with barely any unstructured practice, students are instructed to learn chunks of language by heart without properly understanding it, topics are dated and uninspiring, and it's all marked on accuracy which is all wrong. Think of the last time you had an interaction with somebody who struggled with English. Was their grammar and pronunciation perfect? Probably not, and I bet you didn't feel offended by that. Did they tell you about how many siblings they have and what their hobbies are? I doubt it. But was your interaction useful (to one of you) and did you (both) manage to communicate on some level? Those are the language skills which are valuable.