From their website:
Many of the main cities in the UK are covered by Amazon Prime: Birmingham, Glasgow, Leeds, Liverpool, London, Manchester, Newcastle, Portsmouth and Sheffield.
Amazon Prime Now is also available in some regions of Surrey, Hampshire, Berkshire, West Yorkshire and South Yorkshire. These include Camberley, Lightwater, Aldershot, Bradford, Wakefield and Huddersfield.
Glasgow regions covered include Parkhead, Shawlands and Paisley, as well as surrounding areas, such as Motherwell, Kilmarnock and Cumbernauld.