Saltburn in Teesside and Walney Sandy Gap in Cumbria were among 10 beaches that failed to meet European standards for bathing water quality.
It comes as the Environment Agency announced a record number in England and Wales met the highest standards.
Barrow Council said it would discuss with the agency what actions could be taken to improve Walney Sandy Gap.
Redcar and Cleveland Council said it would co-operate over what was needed to make improvements at Saltburn.
In total, 493 sites were monitored by the agency, which found 86% of beaches and bathing spots reached the European Commission standard, compared with 80% in 2009.
Other beaches that failed to meet standards included Lyme Regis Church Beach, Dorset; Mothecombe, Seaton and Instow, all in Devon; Seaton, Cornwall; Staithes in North Yorkshire; Heysham Half Moon Bay and St Annes, both in Lancashire.
The Marine Conservation Society welcomed the figures but said it remained concerned about pollution from sewage overflows during heavy rain.
It also pointed out that stricter standards were due to be introduced across Europe in 2015.
Environment Agency chief executive Paul Leinster said the number of bathing waters in England and Wales attaining the highest quality status had almost tripled over the past 20 years.
He added: "The Environment Agency is working hard with others to drive improvements and tackle all sources of pollution, alongside beach users, local authorities, farmers, land managers and water companies."