Alex wrote:
Cisterns are really not that expensive to replace, But you could try
sealing the crack with some type of silicone sealent on the inside,
you would need to remove cistern and clean and dry it effectivley
first.

They are expensive if they are in some obsolete colour.
We had dark mink coloured suite (not our choice) and the cistern got broke
by an elderly relative. We claimed on the household insurance. The loss
adjuster said it would cost £750 to have one custom made.
I persuaded ins coy to give me the £750 with which I redid the whole
bathroom in white.