If the Sky box died of its own accord and not through your own fault e.g. dog ate it then if it was me I would be saying to Sky your router is locked down and I cannot get other devices to work since you don't provide the username and password, so the only way to use the service is to use your router, thus forcing me to pay for a replacement is unfair.
Cannot recall if people had the old Be routers working during the switch over phase, but if past that and on Sky full LLU proper the answer may be different now.
Plenty of replacement Sky hubs going on ebay for £10 to £15 which if hard negotiation is not your thing may be an easy and cheaper way out.