It sounds like they are looking at assessing for autism.
I went through this process when my son was age 3 and in primary school nursery. He was subsequently diagnosed with autism.
I was pulled in for a chat after his first few days in school and they explained their concerns; lack of eye contact, not answering to his name, limited social skills, very delayed speech...
They applied for an EHCP immediately which was approved. This outlines the child's additional needs and what the school (by law) must do to support them. It also has targets for the child and what the teachers must do to help them achieve them. It is reviewed annually. My son has 1-1 support and interventions, small group work, sensory room time, that kind of thing.
He was referred to CLASS and MAAT and had an educational psychologist observe him.
He was then assessed for autism. This was a four part assessment.
-Parent interview.
-Teacher interview.
-Classroom and playground observations.
-One to one assessment with me present. For this they had a number of activities planned and I sat in the corner to support him but didn't get involved unless they requested.
Once everything was completed they complied a report with their findings and gave a diagnosis. I think some kind of scoring system was used.
I believe NHS is waiting lists are atrocious at the moment, my friend has been waiting for 2 years since concerns were raised in school and is still waiting for initial assessments. This isn't too important though in the grand scheme of things because a diagnosis isn't necessary for school to be providing appropriate support and a diagnosis isn't vital for an ehcp to be issued.
Hope this helps feel free to DM me if you have any questions.