I think you could come up with a reason to drop any of them, although I'm struggling for Leeds.
Pretty much all of those unis have strong reputations for engineering so there's not much to differentiate on there.
Bath and Southampton are relatively smaller locales, although Bath has stellar travel links which allow you to go to Bristol very easily. If you like that aspect then you wouldn't want to replace them with Bristol because that would reduce your choice for smaller cities. Bath is very good at getting people onto years in industry so if that's a priority for you then I would keep Bath. Typically people would only choose one of Bath and Bristol because of the combination of their similarities and differences so that could be another argument for dropping Bath. Southampton can oversell themselves sometimes so dropping them is an option if you want to be more cautious.
Birmingham has less of an engineering pedigree. A lot of people don't like the city, but the same can be said for Bristol. Assuming you're an international student, Birmingham has by far the best travel links both internationally and to the rest of the UK.
Nottingham is a bit out of the way, but also quite a bit cheaper than Bristol/Bath/Southampton. Travel links within the UK are on a similar par to Birmingham.
I'd say maybe don't drop Leeds because it's reasonably priced, very good travel links, and you have the ability to switch degrees after second year which could be a bonus.