The NHS has not carried out any risk assessment on the health consequence of leaving perishable waste uncollected for up to two weeks. This is not an issue for the NHS.
Domestic waste collection is a local authority responsibility. All issues with regard to domestic waste collection and domestic waste management reside with the Department for Environment, Food and Rural Affairs (DEFRA) and issues with respect to local authorities reside with the Department for Communities and Local Government (DCLG). These Departments have legislative and regulatory powers in this area, something that neither the Department nor the NHS has. Should either DEFRA or DCLG have any health concerns with regard to waste disposal or collection policy they would raise them with the Department.