Not sure how many replies you'll get to this, Nicky, as most people are only too glad to get one job offer, let alone two. Well done you.
Perhaps it depends on how far along your application has gone as to whether you can change your employer's details, but I can't see why they wouldn't accept a new job offer from you. I know they check up to make sure the offer is bona fide etc. but if they haven't already done that, you could slip the new details in instead with no damage done.
I certainly wouldn't let the better offer go as it's what you want and I really don't think you'd have to start from the beginning again. If you already have a case officer, I'd check with him/her about your situation and see what they say. Otherwise just let INZ know what's happened and forward them the full details of the new offer so that it doesn't hold things up for you. I'd hope it wouldn't be too much of a problem.
Good luck. Sorry for the rather sketchy answer.
