The Environment Agency is responsible for 'controlled' water such as rivers and lakes.
Thames Water is usually responsible for drinking water in Westminster. It is regulated by the Drinking Water Inspectorate (water quality) and Ofwat (economics). Some areas have a private supply separate from Thames Water. Check your water bills if you're not sure.
Water in spas and pools in Westminster are sampled and monitored by the Westminster City Council Health and Safety Team. The team also monitors water quality in fountains and parks and in wet cooling towers.