Looking at your qualifications you look able to qualify for IEng, as you are a graduate engineer I am assuming your role is limiting in terms of technical and commercial leadership skills and also using your theoretical and practical methods to analyse and solve a technical and/or engineering problems? I believe these are skills needed to gain CEng and require experience in Industry to achieve. I would recommend going down the route of IEng and then gaining the relevant experience to gain CEng, maybe look at doing your Masters (MEng), maybe do this as distance learning in your own time?
More information is on the links below;
Before starting you should speak to an IET advisor and then register your interest.
I am currently working towards the IEng; I took a different route by completing an engineering apprenticeship whilst completing ONC, HNC, on a day release at college. I am now at uni doing the BEng on a day release so hopefully once I complete this, I can use my experience in industry as well as my qualification to submit for IENG.
Hope this assists you.