The HSWA is the Health and Safety at Work etc. Act 1974: the umbrella statute behind essentially all UK workplace safety law. Its core is a general duty on employers to ensure, so far as is reasonably practicable, the health, safety and welfare of their employees and of anyone else affected by the business, which in a play venue means every child and adult who walks in. The Act is at legislation.gov.uk.
Why it matters more than its age suggests
The Act doesn't tell you how many first aiders to have or how often to inspect the frame. It creates the framework that specific regulations fill in: RIDDOR for reporting, COSHH for chemicals, the management regulations for risk assessment. When something goes wrong, prosecutions are typically brought under HSWA's general duties, and the question a court asks is whether you did what was reasonably practicable. Your documentation is how that question gets answered in your favour.
Inspectors' powers to enter, examine and enforce (see what happens during an inspection) also come from this Act. Fifty years old, and still the piece of paper the whole system stands on. Our complete regulations guide maps everything it touches.