The BME exhibition is a permanent exhibit in the "bubble" at The O2 (old Millennium Dome) in Greenwich.
We went last summer and I really enjoyed it... what do you expect with my interest in music. So last week we blagged some free tickets for an evening entry so we trooped off there again.
There are "pods" off the central core area that are based on various eras in music since the second world war. In them they have lots of museum like exhibits and other stuff to look at, listen too, etc.
Basically after a couple of hours it was obvious the rest of the family were flagging... well my son had wondered off to the guitar studio where you can play various Epiphone guitars... there are some Gibson's on the wall but you can't get them down... including a Dusk Tiger or whatever it's called but I wasn't impressed with the look of it... so we came away but again I think I need to go back and spend more time there. Although you get a ticket with a code on it and you can "remember" bits you didn't look at fully and do it via the website but I haven't had a go at that.
If you are in London and want to spend a couple of hours in a totally music orientated history experience I recommend it.