I am a Chartered Engineer myself (and an examiner!) with the IMechE.
The way to get chartered varies by institution, but all require you to
demonstrate Master's degree level knowledge. Note that 'demonstration' does not necessarily mean you need to have an MEng or MSc, but obviously having an accredited degree will greatly help and check off that item. You then need to have some period of working experience, typically in the 5-10 year range depending on how quickly you get promoted and take on responsibilities. The final exams range all require an interview ranging from 45-90mins but the likes of Institution of Civil Engineers require a 2 hour timed essay on top, and the Institution of Structural Engineers require a
7 hour design exam, which has a very low pass rate, generally around the 28% mark.
The biggest benefit I see is when you need to change jobs or apply for a visa to a new country, or seek equivalence of your professional status somewhere else. In the UK many companies simply will not hire you if you are not a Chartered Engineer and have more than around 5-10 years of working experience.
For things like visa applications, many institutions have "Mutual Recognition Agreements" with engineering bodies in other countries. If I look at Australia one of the pre-requisites for their
Skilled Independent Visa (Subclass 189) which is just about their highest class of visa (highly-skilled, no job offer needed at time of application, instantly grants Permanent Residence), most of the professions require certification from Engineers Australia, of which being a Chartered Engineer in the UK is one route to acceptance.