You can get Chartered whether or not your degree is accredited - you just have to give a bit more evidence (and it may take a bit longer) if not. So don't worry about that.
Whether it is important or not depends on the industry you are going into. For aerospace it may be, but the way to find out is to look at the job adverts and see if it is in the list of requirements. But in practice if it is important your company will help you get it anyway.
Far more important is whether your further degree gives you knowledge and experience which will be genuinly useful to employers. Does it include any work experience? Is it purely research, or is it covering "hands on" skills? Is it going to make your knowledge narrow and detailed or broader? Is the work team based or individual? None of these are "right" or "wrong", but they will define the range of jobs you will be considered for.
Remember that academia is obsessed with academia, and the tiny distinctions between different degrees and universities. Out here in industry we neither know or care: we just want to see interview candidates who are passionate about the subject, know how to use their knowledge to solve real problems, can work well in a team, and will turn up at 9:00 and put in a hard days work. You're most likely to end up as that person if you've done a course which you enjoy with enthusiastic people around you: those are the things to look for.
And again, look at job adverts in the field you're interested in and see what degrees are being asked for. That's the best guide.
(P.S. I have never employed anyone with a Masters degree. All my design engineers - who are a world class electronics research team working in a safety-critical field - have Bachelors or (in one specialist case) PhD. I have interviewed candidates with Masters, but so far the Bachelors students have always come over better. There's nothing wrong with Masters degrees, I got one myself this year, but you need to be sure that it's what your chosen industry and career needs.)
Andy Millar CEng MIET CMgr MCMIhttp://www.linkedin.com/in/millarandy
"The aim of argument, or of discussion, should not be victory, but progress." Joseph Joubert