The best known case is Moffatt v Air Canada, decided by the British Columbia Civil Resolution Tribunal in February 2024. A customer asked the airline's website chatbot about bereavement fares after his grandmother died. It told him he could apply for the reduced fare after travelling, within 90 days. That was wrong.
Air Canada argued that the chatbot was responsible for its own actions and that the correct information was elsewhere on its site. The tribunal disagreed. It said Air Canada could not separate itself from the chatbot built into its own website, and that a customer can't be expected to double check one part of a website against another. It awarded around 650 Canadian dollars in damages, plus interest and fees.
This is a Canadian small claims decision, not UK law. But the principle is easy to understand: customers will treat what your chatbot says as what your business says. Plan on that basis.
There is also the risk to your reputation. In January 2024 a customer got DPD's chatbot to swear and call the company names, and the screenshots spread widely. DPD said the problem came after a system update and switched off the AI part of its chat.
Assume that anything your chatbot tells a customer will be treated as a promise from your business. Set it up so it only says things you would happily put in writing.