Another UK Band 2 owner here.
My strap split for no reason back in March and I sent the Band off for repair but got it sent back to me almost immediately after the warranty centre received it, citing 'physical or intentional damage' which wasn't eligible for warranty service. So I left it in it's packaging in a draw for 2 months.
After reading this thread and a few others, I decided to request a call-back from the support site and spoke with a guy a minute later. I told him about my previous service request and how I recently found out that the UK warranty centre(s) was rejecting these cases because they didn't know that they were indeed included in the warranty, like how customers in the US have theirs replaced immediately.
The guy on the phone said I was right and that there has been a change in protocol with these cases - split straps are covered by the warranty (although I doubt they would be if the strap had completely broken to the point where it's fallen off as a separate piece). He said that escalation services would be passed the details of the case so that they can 1) unvoid my warranty (it got reset to expiry year 1900 after the first servicing claimed it was physical damage), and 2) set up a new order that exchange my current Band for a new one (not sure if brand new or refurb).
I've just been emailed a new shipping label a few minutes later and will be posting off the box with my Band 2 and charger some time tomorrow. The guy said that I would expect to receive the working product about 7 days after I send it off to them via UPS.
TLDR: If you've got a split strap, make sure it doesn't complete break apart. Keep it safe and send it off for warranty repair as a "Other: design fault, rubber strap split" problem. If, for some reason, they send it back without repair, just go to the support site online, "Contact Us" and start a chat with an agent or enter your phone number to request a call-back to speak with them in person. Explain your situation, citing the design fault that many users have experienced and how the warranty centre didn't know it was an issue that is in-warranty coverable, and they should sort you out with the escalation service to correct that.