Three good links here for you:

https://www.carersuk.org/help-and-advice/work-and-career/other-rights-at-work/your-right-to-flexible-working

http://www.acas.org.uk/index.aspx?articleid=1362

https://www.workingfamilies.org.uk/articles/flexible-working-after-30th-july-2014-a-guide-for-employees/

You have a right to ask for flexible working or accommodation of your situation but they are not obliged to accommodate your request if it adversely affects their business for example.

It might also be useful to phone the Parent to Parent service at the National Autistic Society for some informed support. Parent to Parent (P2P) is a UK-wide confidential telephone service providing emotional support to parents and carers of children or adults on the autism spectrum. The service is provided by trained parent volunteers who are all parents themselves of a child or adult on the autism spectrum. Appointments with the service can also be made via the Autism Helpline 0808 800 4104

Hope this is useful.