FYI I found the UK river vector file here: https://www.ordnancesurvey.co.uk/business-and-government/products/os-open-rivers.html

On this website there is also a lot more..

However, I am still looking for the UK basin GIS file..

FYI a colleague of mine suggested me the following website, where you can find the UK (detailed) river network: https://www.ordnancesurvey.co.uk/business-and-government/products/os-open-rivers.html

On this website there is also a lot more..