@handmademitlove the LA is right, they can’t force CAMHS to respond. They don’t have the power to force them. They can, however, request advice and information from them. As a public body, CAMHS must respond within 6 weeks. And if the LA genuinely can’t seek such advice within the timeframe from the NHS, they should commission an independent assessment.
As an aside, you should be more specific in your request. If you say CAMHS, it could be anyone from CAMHS (e.g. a band 2 support worker). Instead, you should say psychiatrist or clinical psychologist (or the title of whoever you would like the LA to seek advice from).
@Cinnamoncupcake it can be normal in some cases.