My undergraduate degree took me 5 years. I called myself an engineer after that. I became charter a couple of years after my PhD, so twelve years to become recognised as an engineer! I think you can call yourself an engineer after you have graduated from your undergraduate degree.
University courses are 3 years for a BEng and 4 years for an MEng.
Most graduate enter into a graduate training scheme run by an employer.
Hope fully they will provide the graduate with training which will meet the training requirements for CEng.
Once the training requirements are met, an interview with the relevant issuing organisation such as the IET IMechE, ICE etc. It usually 3 – 5 years to get your chartered engineer registration.