Specialisation is mostly from experience during your career, masters years help with starting to specialise but you won't suddenly be an expert. Different universities have different masters courses, mine offers structures, bridges, geotechnical, water/environmental and management. Currently I'm looking more towards structures relating to highways (on my placement im working in a highways structures team, this office also has a buildings structures team).
The MEng is an integrated masters, tends to be that you can pick and choose modules whereas an MSc keeps you in specific modules, you wouldn't do an MEng followed by an MSc, in my masters year since I'm in the MEng I can choose any MSc modules.