Hi ma6tt, I have some experience in this area as I am involved in the recruitment of experienced and graduate civil engineers for the Tier 1 company I work for in London and hold a BEng in Civil myself.
Firstly both bachelors are accredited to Incorporated level, this means which ever degree you choose to do, if you aspire to become a chartered engineer in the future you will need to do an accredited MSc in civil, construction management or similar. This will put you on par with graduates who have obtained a MEng degree. Its actually a bit cheaper to do the BEng+MSc route circa £4K.
As a employer I would have no preference over either university's and you would be considered for employment if you gained a 2:1 or first.
Personally I would go to either Greenwich or Brighton and do 4 years study to get both the undergraduate and postgraduate rather than doing 4 years in Brunel for just the undergraduate degree, you will have less debt, more qualified to chartered level and therefore more employable.
Ray