I'd guess that around £1000 might be the lowest figure that the council would regard as acceptable (if, indeed, they will actually allow any discount). That's because they might end up paying around £400 in collection charges if they have to hassle for the full amount.
I'm not entirely sure that I agree with JD33's statement that "Councils are unforgiving in this respect". While councils are obliged to carry out their statutory duty to collect Council Tax, they do seem to have some leeway. Earlier this year I complained to my local councillor that an error by the council had resulted in them giving me 100% discount on my Council Tax for a full year and then, when they looked at it again, billing me for the full year's tax in one go (with no option then available to stagger my payments). A bit of pressure from the councillor resulted in the council writing off my Council Tax bill for the entire year!