The Health and Safety at Work Act 1974 requires employers to ensure the health, safety and welfare of their staff and others present in the workplace (including schools) meaning they should seek to protect against excessive working temperatures.
Similarly, Regulation 7 of the Workplace (Health, Safety and Welfare) Regulations 1992 requires employers to ensure that temperatures in workplaces should be reasonable.
The Department published updated guidance for new school buildings in 2018 that covers indoor temperatures and measures to reduce overheating. This can be accessed here: https://www.gov.uk/government/consultations/ventilation-thermal-comfort-and-indoor-air-quality-in-schools. The Department is also working with wider industry to develop good practice in response to climate change to ensure we have a sustainable school estate.
Guidance for schools during a heat wave is widely available for both indoor and outdoor activities including practical advice that includes relaxation of uniform policy. It is for the governing body of a school (or in the case of academies, the academy trust) to decide rules relating to appearance, including whether there should be a school uniform.
Public Health England guidance for teachers and schools for early years provision during heatwaves is available at: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/428850/Looking_After_Children_Heat_PHE_AC_AB_Publications_MP_JRM_FINAL.PDF.