Success! Called them up (01628 450 660 opt. 4) and the chap said it has been assigned yesterday, and he could send me a text with it now, which I have now received. I asked him if there was any risk of it changing before collection day and he said it shouldn't because we're so close to the day now. But he did say there is a small chance that they can change, which is why they don't text them out in advance unless asked.
I'm going to go ahead and get the insurance though. In the unlikely event my reg changes, I'll call the insurance company and hopefully they'll let me switch it.