Understanding song lyrics is a real challenge so I wouldn't worry about that. When you say "speeches", are you actually listening to formal speeches (like TED talks) or are you simply listening to people speaking/chatting? My recommendation with using radio to improve your English comprehension usually revolves around getting used to the rhythm and cadence of the language. I suggest to my students that they have the radio playing whenever possible but not to to actively listen to it. Do other things. Have the radio on while you're cooking, cleaning, showering etc but there is no need to sit down and listen intently to it.
You said you've been listening to UK and US radio. Perhaps, for a few weeks, you should concentrate on one or the other. The differences between the two might be relatively minimal in certain respects, but there are enough differences to confuse your ear.
When I lived in Spain, I found a "talk" radio station and I switched it on first thing in the morning and turned it off last thing at night. I didn't once sit down and concentrate on the words, I simply let the speech wash over me and around me. It took a few weeks but eventually I realised that I was understanding well over 50% of what I was hearing and, depending on the speaker, sometimes more like 80%. The Spanish are well-known for talking at a million miles an hour so I was very proud of myself!