If you don't have a will yet, get one sorted out and include your funeral wishes. If you don't and nobody makes any arrangements, your remains will be classed as an 'unclaimed body' and reported to the Council. The first thing the Council will do is contact relatives and advise them to make arrangements.I own the plot in the local cemetery where mum is buried so will go in there. Just a case of making my will out and stipulating what I want I suppose.
If they flatly refuse then the council will do it as a last resort and will claim the costs directly from your estate. If your Council uses burial you will be buried in an unmarked grave (i.e no headstone). The grave will be used for further burials.