I have a friend who had this situation last year, although the unconditional offer didn't come through until February. None of his 5 offers did.
Three things - are you sure that this uni won't also give you a conditional offer which you can use as insurance? You may find that, if they do, it is quite a nice low one. They may not rush to do it but it might still happen.
You don't have to make any decisions yet, do you? Don't rush into it.
And finally... my friend rejected his unconditional offer in the end, as he didn't really want to go there, tempting as the offer was. And then the night before his A level results they got back in touch with him to tell him that they'd still take him.