I think if you apply to any university they'll strongly recommend that you should be doing the MEng instead. The BEng isn't enough to even get chartered is it? So you'd need to do another degree anyway.
If the unis I've looked at are any indication then many offer an integrated masters programme but most students will be on the bachelors route. At the institution where I work (Uni of York) many more BEng degrees are awarded than MEng.
You don't need the Masters degree to be a chartered engineer as far as I know.
If you graduate and gain enough experience on the job (probably more cost effective than being at uni for another year) to be considered to have an equivalent standard of education I believe you can become a CEng with a presentation.