Southampton is considered very strong for engineering, certainly on par with and possibly "better" than several of those other universities you have noted. Loughborough is a good option imo as they're generlaly considered well for STEM courses and have good connections to industry. Bristol has a lot of nearby aerospace industry and probably some connections with the university that you might be able to exploit there.
Otherwise my impression is Warwick is a bit lesser than the other universities for engineering - it's best known for its mathematics, CS, and economics departments. I believe Bath has a strong civil engineering course but I'm not familiar with it's mechanical engineering department.
If you wouldn't mind applying to Scotland (and not just England) Strathclyde and Heriot-Watt are very well regarded and particularly have excellent connections to industry and graduate placement records - they are quite highly recruited from by engineering firms as I understand.