Filter or filter-element designated for Modified Electro-Dialysis (MED) purposes characterized in that the filter or filter-element comprises a porous, ceramic, mainly uniform material with functional, preferably ion selective groups grafted onto the inner, porous surface of the ceramic body. The outer surface of the filter or filter-element may be completely or partly covered by layers of porous, ceramic membranes with a pore size of less than 1 .mu.m and thickness less than 1 mm, and/or anion, cation or bipolar groups or membranes. The thickness of the filter-element is larger than 1 mm and has pores of size larger than 1 .mu.m. The invention also relates to a method for the manufacture of such a filter either continuously by tape-casting, extruding, rolling or calendaring or single-bodied by casting, pressing or forging, of a paste containing a non-conductive, ceramic material. The body is then sintered and finally grafted with functional, preferably ion selective groups for one or more specific ions or groups of ions, onto the inner, porous surface of the ceramic body. Use of the filter or filter-element for filtering ions or complexes of heavy or precious metals from water is also claimed.