I have some over-ear headphones and they are actually quite good at blocking out external sound. Annoyingly, the headband snapped (entirely my own clumsiness) so they no longer stay in place unless I wear my buff over the top of them, which looks ridiculous!
They were also a John Lewis purchase -
their own-brand H1 - surprisingly good for the £20 I paid for them. But of course they have now discontinued that line, the sods, or I would buy a new pair with my voucher.
My other earphones are a set of Sony wireless - but not "true wireless", ie the ear buds are linked by a wire. I hate them - the sound quality is good but the weight of the inline battery and remote means they fall out of the ears very easily, especially if you don't keep your head upright. And they don't stay in at all when running. This is the main reason I'm keen on the "true wireless" type.
Good point about the glasses.