I would disagree that Bath has better graduation support than Manchester.
Manchester offers CV, covering letter and interview practise 1 on 1 either from a general employment support point of view or from the ChemEng school themselves. Not only this but there are companies that come into the University and give intensive information into their company as well as giving employment opportunities to the students.
Any Russell Group University will be an excellent choice. As long as the course is IChemE accreditied, its is often not too much of a difference as to where you graduate from in between the Russell Group universities. Obviously, Oxbridge is a level above them and other unis are a level below. Therefore, you want to look at the course structure i.e. what you will be studying/choice in electives etc. and definitely look into doing a Masters course with Industrial Experience. Both will give you a significant boost when it comes to applying to jobs.
P.S. This is my own opinion but the labs and pilot plant at Manchester as well as the new Engineering building being built, put it above Birmingham on my list when I was applying.
Even the grade you get at University is only super important if you are looking to apply for a design-based job i.e. in a design office where you will be using more of your degree to design processes. If you are interested in going into process engineering, i.e. problem solving real-life issues on a plant with direct impacts on performance and profit, the companies are looking for the applicants to have a good mindset and are good communicators, more than people who have a 1st Class Honours degree.