You are. The CMA says this applies even if someone else designed or provides the AI agent. Breaching consumer protection law can lead to enforcement action, and the CMA says fines can reach up to 10% of worldwide turnover, along with compensation for affected customers.
There is a well-known example from Canada. In Moffatt v Air Canada in 2024, a British Columbia tribunal found the airline responsible after its website chatbot gave a customer wrong information about bereavement fares. The tribunal found Air Canada did not take reasonable care to ensure its chatbot was accurate, and ordered a partial refund. It is not a UK case, but it shows how a business cannot blame its software.
Only let AI answer from information you have checked and approved, such as your own website pages and policies. If it can't find the answer there, it should say so and offer a person. A polite "I don't know" is far cheaper than a confident wrong answer.