It sounds like a Raleigh Twenty (AKA Raleigh Shopper, Raleigh Folder, &c). Raleighs were sold under many different names, and the Twenty was no exception. I've heard of Phillips, BSA, and... oh, I forget the whole list now. I wouldn't be surprised to see the same bike badged as a Hercules, Rudge, Triumph, etc.

They are not rare, but they have a devoted following. If it's in nice condition you will have no trouble finding a buyer. In my area a well preserved one might sell for $200 or more; one in rough condition might still bring half that.

Here's a web page about them. But if you google "raleigh twenty" and look at photos, you'll know pretty much instantly whether that's what you have.