This morning I and a student at the university of Kent at Canterbury did some spectroscopy on a Webb's Alexandrite wine glass. I had established previously that the body of the glass was radioactive, so the yellow is caused by uranium. W.W. Weyl in his book "Coloured Glasses" (ISBN 0-900682-06-X), gives three possible ingredients for purple glass; manganese, nickel and titanium. The maximum spectral absorption of the purple in the wine glass was near 575nm, which is consistent with titanium, but not with manganese or nickel. He stresses the difficulty of reducing titanium to the purple (+3) form. However, I suspect that re-heating in a chemically reducing atmosphere, or even covering the edge of the glass with oil and re- heating it, would form purple Ti3+.
I suspect, therefore, that Webb's Alexandrite is based on uranium and titanium, though X-ray fluorescence would be needed to confirm this.