Once your DC has a diagnosis then they are covered by the Equality Act '10 and the Gov SEND Code of Practice.
It's a long doc and not all sections will apply to you.
assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/398815/SEND_Code_of_Practice_January_2015.pdf
School have a statutory requirement to produce an IEP - Individual Educational Plan. Do not let the school tell you otherwise.
This should take the recommendations from the clinical diagnostic report and any other observations eg school / home. This should be reviewed termly - what works / what doesn't.
It should include educational, social and behavioural aspects. The SENCo should produce this.
If the school are pushing back on the diagnosis, ask them why.
You had the assessment and diagnosis from a clinical psych. Unless they are accusing the clinician of fraud, then the diagnosis stands.
Teachers have little SEND training, unless they go on to further qualifications and usually this is for SpLDs (specific learning difficulties). They are in no position to question the ASD diagnosis. That would be a very interesting tribunal.
The diagnosis cannot be removed. A clinical psych will be trained to undertake all parts of the ASD testing, scoring and diagnosis. Ed psych's may have further training but they are not qualified to undertake all parts of all of the tests, scoring or diagnosis for ASD. Just in case the school offer to bring in another clinician.
There are strict rules about how many times a child can be tested / retested during a given period.
Money (or lack of) is not a legal argument for the schools not to provide the accommodations from the clinician's report.. See SEND Code.
Re EHCP - these are usually granted for DC who difficulties are so great the school's budget cannot meet their needs. Not all DC who have a diagnosis need an EHCP. The diagnosis and IEP should be enough.