the other thing is, most funeral directors will take installments, if it can't be paid right away (let's face it, who has 2K + just lying around anyway?)
The problem is of course, that if the council have to arrange and pay for things, it probably wont be as you/she wanted it to be (for example, where is she now? If she's at the funeral directors, they may not use those ones, they may not do a cremation (although it seems likely i suppose) She will have a complete paupers funeral which may not be very nice, not presided over by religious person, no ceremony, no flowers etc etc)