In order for AI to diagnose cancer, the country's National Health Service would submit reams of genetic and medical information to internet companies familiar with combing over data at a large scale. In other words, they could be profiting directly from handling sensitive personal data normally managed by a government body. May outlined plans for a data ethics council back in January, but that isn't likely to completely offset concerns the data might be abused or fall into the wrong hands through a breach.
The funding pledge could easily produce a mixed reaction, for that matter. It could save both people and money, but critics may argue that the NHS doesn't receive enough funding for its existing operations. Why spend large sums developing uncertain technology when there are hospitals that could use those funds right now? AI cancer diagnosis could prove incredibly valuable if successful, but not everyone is willing to accept such a big "if" when patients' health is on the line. Still, it's rare to see any government commit to AI-based medicine in such a public way -- it might get other countries following suit.