You do have legal protection here, even as a self‑employed contractor. The organisation is wrong to say you have no rights. The relevant law is the Health and Safety at Work etc. Act 1974. Section 3 of that Act says employers must ensure, as far as reasonably practicable, that people who are not their employees are not exposed to risks created by the employer’s work activities.
A mandatory laundering system is part of their work activity. If that system repeatedly damages uniforms because it is poorly supervised, that is a foreseeable risk they are responsible for preventing.
You can also refer to the NHS Uniforms and Workwear Guidance and the organisation’s Infection Prevention and Control policy. Both make it clear that if an employer requires on‑site laundering, they must run the process safely and in a way that does not cause avoidable harm. CQC Regulation 15 also applies, because it requires providers to maintain equipment in a way that avoids unnecessary damage or loss.
There is also a financial issue. If you are repeatedly forced to replace uniforms because of damage caused by their mandatory system, those costs become work‑related expenses. If those expenses reduce your effective earnings to below the National Minimum Wage, the organisation can be held legally accountable. HMRC can treat you as a “worker” for minimum‑wage purposes if the organisation controls your working conditions, including infection‑control rules, uniform requirements, and laundering processes.
In that situation, they cannot impose compulsory costs that push your pay below the legal minimum.
You are not expected to keep replacing uniforms because of a compulsory process you do not control. You can request reimbursement for the damaged uniforms as a direct financial loss caused by their system, and you can point out that Section 3 of the Health and Safety at Work Act, the IPC policy, and minimum‑wage rules all support your position.