If there was a need for a DPM to be installed the chances are that this will not totally stop rising damp. The only potential problem will be that once the cavity is filled the walls will only have one surface for evaporation of trapped moisture to escape.
Have a word with your neighbours who have had their cavity filled and see if they have any damp problems.
For readers looking for related advice please see our cavity wall how to projects which has a bunch of useful articles and information on damp issues and fixes, vertical Dpc, insulation of cavities, cavity trays and lintels and pumped cavity walls.
DIY how to tutorial projects and guides - Did you know we have a DIY Projects section? Well, if no, then we certainly do! Within this area of our site have literally hundreds of how-to guides and tutorials that cover a huge range of home improvement tasks. Each page also comes with pictures and a video to make completing those jobs even easier!