The school is responsible for education not medical needs. A school that refuses to administer meds is not breaking any law. You don't like that. We get that. But it's still the way it is. And the way it will stay.
I do not think that is strictly true. The government says this:
Supporting a child with a medical condition during school hours is not the sole responsibility of one person. A school’s ability to provide effective support will depend to an appreciable extent on working co-operatively with other agencies. Partnership working between school staff, healthcare professionals (and, where appropriate, social care professionals), local authorities, and parents and pupils will be critical. An essential requirement for any policy therefore will be to identify collaborative working arrangements between all those involved, showing how they will work in partnership to ensure that the needs of pupils with medical conditions are met effectively.
16. Governing bodies must make arrangements to support pupils with medical conditions in school, including making sure that a policy for supporting pupils with medical conditions in school is developed and implemented. They should ensure that sufficient staff have received suitable training and are competent before they take on responsibility to support children with medical conditions.
Headteachers should ensure that their school’s policy is developed and effectively implemented with partners. This includes ensuring that all staff are aware of the policy for supporting pupils with medical conditions and understand their role in its implementation. Headteachers should ensure that all staff who need to know are aware of the child’s condition. They should also ensure that sufficient trained numbers of staff are available to implement the policy and deliver against all individual healthcare plans, including in contingency and emergency situations. This may involve recruiting a member of staff for this purpose. Headteachers have overall responsibility for the development of individual healthcare plans. They should also make sure that school staff are appropriately insured and are aware that they are insured to support pupils in this way. They should contact the school nursing service in the case of any child who has a medical condition that may require support at school, but who has not yet been brought to the attention of the school nurse.
Parents should provide the school with sufficient and up-to-date information about their child’s medical needs. They may in some cases be the first to notify the school that their child has a medical condition. Parents are key partners and should be involved in the development and review of their child’s individual healthcare plan, and may be involved in its drafting. They should carry out any action they have agreed to as part of its implementation, e.g. provide medicines and equipment and ensure they or another nominated adult are contactable at all times.
(https://www.gov.uk/government/uploads/system/uploads/attachmentdata/file/638267/supporting-pupils-at-school-with-medical-conditions.pdff__)
_
So going into school to administer medication is not a parent's responsibility.