I don't think that would meet the public interest test, though.
There is a statutory scheme for criminal injury compensation (I think) but I don't think it relies on a conviction being obtained. If, for instance, you're the victim of a machte attack and you lose a hand I can't imagine that you don't get paid out if they don't catch the perpetrator.
The whole subject of "compensation" for bereavement is morally problematic, in my view. It shouldn't be a general principle of law that families are compensated financially for the loss of a loved one. You can't compensate for loss of life and I don't think that the law should be trying to do that. It's seedy, in my opinion, that a life can be compensated for with money.
There is a valid reason for compensation in the case of people who are left with long term health issues which is obviously acceptable. But, having said that......we have the NHS which will bear the brunt of that financial burden so people won't be paying for it themselves.