Hooray, after 3 false starts have finally found the death of Elizabeth. She died on 9th December 1864 in the Union Workhouse, Mile End.  I am about to put a copy of the certificate on the Tribal Pages website.  Interestingly, the certificate shows that her husband, Thomas Haines, was still alive then, though the 1841 & 1851 censuses do not show them living at the same address – must explore Thomas Haines a bit more I think!