Is this the referenced study?
https://pubmed.ncbi.nlm.nih.gov/38592388/
Acetaminophen (paracetamol) depletes glutathione, the liver’s main antioxidant and detoxifying molecule. So any use of this drug carries a risk because harmful substances will be present in your body for longer or at higher levels than if it was completed avoided.
Avoiding it completely in pregnancy is a good idea. Along with avoiding many chemicals, dyes, and other pharmaceutical products as much as you can.
Autism is likely caused by many factors, genetic ones are not acting alone, there can still be dozens of environmental factors that increase the chance of developing autism to different severities, depending on your genetic predisposition.
Here is an example of a paper that does happen to find an effect:
https://pubmed.ncbi.nlm.nih.gov/26688372/
Dr Alison Cave’s quote in the OP is inaccurate, as there are studies that show an effect. Her quote, in her position, is a result of corporate capture of the MHRA regulatory body.
Regulatory bodies such as the FDA/WHO/MHRA receive money from industry, it’s called corporate capture. The studies that are funded by industry are designed in such a way that makes it likely they will get the results they want so they can continue to sell their products.
The study included mothers of all ages, as we age our livers become less efficient, so likely the risks of using paracetamol in pregnancy might increase with maternal age. Just as you can design a study that shows there is very little to no observable statistical risk, you can design a study that does show there is an effect! As an example you could try to find an observable effect by studying older mothers who only used paracetamol multiple times in the first trimester...
All drugs pose a risk, nothing is 100% safe. Trusting in our regulatory bodies, and in single research studies might not give us the best chance at a healthy life.
I personally, would not reach for a fluorescent yellow Lemsip, or paracetamol tablet for a cold or a mild-headache at any time. High fever in pregnancy is more complicated, and I hope that the government fights the corruption in our regulatory bodies so that we can start to rely on quality scientific papers to inform ourselves.
Good luck to all mums trying to make good decisions for themselves and their children in our modern world, which is rife with corruption and harmful environmental substances and products.