Student found guilty of plagiarism is also academic at other university
This may be covered by privacy law in UK as it would be in US. You need to consult with a lawyer before you take any action that isn't already embodied in your policies, which I assume have already been vetted. 

If you are permitted to inform the other university you should also consider whether you are liable to civil action if you do so. But your lawyer will have advice about that as well.