Graduate Scheme

I am a second year Mechanical Engineer at the University of Birmingham, doing a BEng. I will hopefully graduate next summer. I am looking for a Graduate Scheme, not fully sure in what sector, but I like the Energy sector the most for now, companies like RWE, EDF, Centrica, BAE Systems (but they probably only accept British nationals), Babcock, so anything Nuclear related or Renewable Energy related. I am of Italian origins, but thinking of getting British citizenship.
Could someone give me an insight on what are the best companies for a graduate scheme for someone with a Bachelor's degree, in the sectors I am interested in? I kinda would also enjoy to travel as work, so anywhere in the UK, Europe, I know someone who is a Mechanical Engineer and works for RWE and they get a lot to travel, being in the technical safety department.
Thank you in advance.

For companies to look at, as well as those who own or operate energy generating assets (some of whom you have listed), check out the various engineering contractors also involved in this area (e.g. Atkins, Jacobs, Mott Macdonald, etc.) as well, and also those that manufacture key equipment (e.g. turbines, wind turbines, etc.). However, just to make you aware, some companies may prefer, or only recruit, masters applications,

I kind of don’t want to work for a consultation company. That’s why I an sort of not looking for them.
I know some companies only accept graduates with master’s I just want to start working, I hope to get my master’s while working part time, to become CEng.