One issue is that the diagnostic criteria to meet overlaps with several other conditions, and as autism is becoming more well known with more resources in promoting awareness & support and less stigmatised, the more that's going to be considered before other conditions both by families and professionals. Add on that what can help an autistic child can also aid children with those conditions, if not as well as care for their condition, as well as many children who are just not handling the stress of the current education system, and the spike and contrast between what is experienced and stats isn't surprising.
Academic estimates are 1-2% of the population are autistic.
Same estimates put FASD at the same to twice as common, but we'd never know it just looking at SEN stats or parent conversations, because it is heavily stigmatised. The only time I've seen it discussed is with Children in Care. FASD has both heavy overlap in symptoms and a comorbidity of FASD is ASD. It has far fewer resources and ability to be diagnosed with only a couple centres in the whole country for those diagnosed after infancy, and there is still a lot of myths about it like requiring the 'sentinel facial features' to be truly FASD, even though that presentation makes up only 10-15% of those affected. Many of the things for ASD help those with FASD, though social education and things like memory tend to need very different care for the best support.
OCD, clinical anxiety, and trauma response dysregulation in children also has significant overlap, and so do some learning and language disorders. Stress can also present with some of the symptoms like sensory overwhelm and sensory seeking, a strong drive for routines, and social difficulties.
Another issue is how data is gathered on the numbers. All of the reporting varies a lot.
Some schools only report those who have an official diagnosis, others will report any child in the very long screening and diagnostic process - which in some areas, including my own, it is strongly recommended any sibling of a child who gets a diagnosis also goes through the screening, and others report any child who is getting Social and Emotional support recommended for ASD children as ASD.
Same with wider research - some is based on official diagnosis with a buffer for a portion of the waiting list and undiagnosed, some track and include self-reporting, some is based on extended same classroom observations and family discussions to see how many children would meet the diagnostic criteria which tends to be a strong standard when looking at child diagnoses though it obviously as issues when we're looking at wider populations (and obviously for things like FASD, there is far more grouping by communities than we'd see for something like ASD, in areas with a lot of alcohol issues, FASD rates have been reported as high as 7% of children in the area schools).