Theoretically you can keep anything.
Realistically there are restrictions that you have to deal with. Without a DWA licence you can only legally keep animals not on the DWA list and additionally certain animals are subject to CITES restrictions.
There's also the fact that some animals would be impossible to source (e.g. some of the smaller (wild) cat species can be kept without a DWA licence, but have never/hardly ever been kept in captivity).
Interestingly, there' some really cool mammals that can be kept without a DWA licence and are sometimes available in the UK (to some extent or other)- Coatis, Armadillos, Raccoons, Civets, Skunks, Genets, and many, many rodent species