No.
The only “insurances” which are legally required are motor vehicle insurance and employers liability compulsory insurance - https://www.gov.uk/employers-liability-insurance
Any other types of liability insurances are entirely optional on the part of the party seeking cover and the insurer may invoke what ever terms and conditions within the policy as they see fit.
The presence, absence or terms of a policy have absolutely no relationship to the liability of the party that has inflicted loss. Harm or damage upon an other. The RESPONSIBILITY to do no harm exists whether insured or not.
If a PC does harm to another and the PC’s insurance refuses to cover the recommence, the damage, harm, loss still exists as does the responsibility for it.
All it means if a PCs policy refuses to pay out is that the PC has paid for an inappropriate policy or that the terms of the policy have not been complied with.