Metal sheet inside bottom bracket on frame: can I remove it? I have an old frame (60's vintage), into which I'm trying to install a modern sealed cartridge bottom bracket.

I've got a bog-standard Shimano BB-UN55 with diameter 68mm, which should fit the frame. Indeed, if you hold the cartridge up against the bottom of the shell on the frame, it's definitely the right size (phew).

However, I can't actually screw in the cartridge to install it. It turns out this is because there is a sort of wrapped around metal sheet inside the shell, which starts about 12mm (1/2"?) in on each side and the Shimano cartridge only gets narrow in the middle about 17mm from each end.

I assume this sheet is just to stop grot falling into the non-sealed bottom bracket from the frame tubes and I can probably pry it out with a screwdriver or similar, but wanted to check: should this be there for some other reason?

Thanks!
Based on your description, its some kind of "cover" that would stop water dripping down the seat tube from sitting on the BB axle.

Seat tubes are notorious for leaking, mostly because the slot at the back of the seat post is an entry point for water, which then weeps downward by gravity and eventually drops through the weld breathing hole between the BB tube and the bottom of the seat tube.

In theory water should continue through and drip out the drain hole at the bottom of the BB, but some bikes don't have that so water collects.

On the other hand some frames have ridiculously oversized cutouts like this which allow a lot of water to spray up off the front wheel:



So your metal shield could be doing the same job for water from the road.  Above picture shows a white waxy plastic liner.

So in theory your modern BB cartridge will have a shield purely because it IS a cartridge already and is much more resistant to moisture.