@Laura Yes, the Zurich warranty is of little use when it comes to snagging, not much worse than the NHBC warranty. I am afraid that new homes or more specifically land transactions are excluded from the Sale of Goods Act 1979 and the Supply of Goods and Services Act 1982. However, you are still protected by contract law and common law so you can pursue the builder through the courts. Before you do that it is worth trying to establish whether the business is viable and would be able to pay as I am assuming this is not a mass builder. You can use the Small Claim process and this only costs £35 if the cost is less than £10,000. You will need someone to cost the remedial work for you. And before you do this you need to give them the opportunity to put the problems right before you start legal proceedings.
Comment on What is a snagging list? by Tony