No the act of applying elsewhere shouldn't void your current place, with these 'integrated masters' courses which I presume you are on as you say its a 4 year option, the usual rule is you are guaranteed a place at your existing institution if you achieve a certain score (eg a 2:1) in your first three years. I expect that you are doing an MEng where you get awarded BEng if you leave at the end of 3 years and MEng at the end of 4. I expect you would need to tell your uni you are applying elsewhere as you would need an academic reference. As regards the weighting scheme of marks, I am just making an educated guess, but I would imagine if you leave Southampton after year 3 and do year 4 at another university, then you will get given a score from Southampton and a score from your other university just based on that masters year, eg your CV may say something like BEng (Soton): 2:1, MEng (SomewhereElse) 1st. If you stay at Southampton you will just get one grade for MEng and you put it down on your CV as an MEng. But you would need to check with the institution to which you are going.
One thing to watch for is that although an MEng is usually sufficient level to get you chartered, in industry it's not regarded as high as an MSc. So if they will accept you off 3 years at Southampton, only an MSc programme rather than an MEng then this may be good although the level could be a steep learning curve.
I will allow engineering students to give you better advice as I was an economist myself, however I lived with a house of engineers and a lot of my friends did Civ Eng and Eng Geology so I've heard a lot of their chat.