quote .............."is the crystal on the base of wine glasses from crystal of Edinburgh always cut or can it be plain? Most of the designs I have seen are cut".
Assume Marianne that you are referring to the foot of the glasses - the answer is that feet can be both cut and plain - although looking at designs in the this link........
http://www.discontinueddesigns.co.uk/category.aspx?categoryid=7 ... I'd agree with you that the majority are plain (uncut). If you go to either the second or third design, on the attached sit, and blow the image way up, you should see a back stamp on a plain foot (to the right in the image).
Bernard is quite correct - however, to me it seems rather a contradiction ......on the one hand to have a rather lavish looking silk lined box - and on the other to omit the makers name - but that's commerce for you.
Should the box be lost or disposed of at some time, then the pedigree of these pieces will be lost - since as you have discovered, finding the pattern on the screen can be nigh on impossible. Made all the more difficult as so many manufacturers created a pattern/design that incorporated a 'fan' cut.
Whatever you do, just don't lose the box.