While public liability insurance may not be a legal requirement, it is nearly always a contractual requirement in the construction industry.
Most reputable businesses will insist you have public liability insurance in place before they enter into a contract with you. You will also need to be able to show them a copy of your insurance certificate.
If you had public liability insurance prior to the contract, and either didn’t renew it or cancelled it for some reason, that would put you in breach of contract.
It would be reason enough for the client to withdraw from the contract. In a worst-case scenario, they might sue you for damages, due to you breaking the terms of the contract.