There isn't actually a lot of chemistry involved in chemical engineering; what there is, is physical chemistry (taking thermodynamics into the chemical kinetics and statistical mechanics regime more) and the rest is mainly lots and lots of fluid/mass/heat transfer, along with process/control engineering, none of which are covered in a chemistry degree.
That said I believe UCL have a chemical engineering masters which with the correct options fulfills the initial (BEng level) requirements for CEng if you have a non-chem eng first degree with whatever the Chem Eng society thing is.
But like others have said, if you want to be an engineer, do an engineering degree. If you want to do a bit more chemistry than you would otherwise look at joint honours or similar courses (I think Strathclyde have an industrial chemistry and chemical engineering joint course which fulfills the CEng reqs while also have a fair bit of chemistry content).