So its not actually a Sussex University laptop.... ?
I would be amazed if it did work if that's the case .... I work for BSUH NHS and Zero external Laptops etc connect to the domain its has to be our kit, NO exceptions.
Your laptop is not recognised by the domain.
Has it been a while since you used it at work ?
Removing and re-adding to the domain always works for me... but you need Admin to do that...