Some flooding of low-lying land and individual properties is possible along the north west coast from Friday into Monday and along the north east coast on Friday and Saturday.
The east coast and parts of the south coast, plus Devon, Cornwall and the Bristol Channel could also experience local incidents from Saturday into Monday.
Strong winds on Sunday into Monday may also continue to affect communities along the south west and north west coasts with a risk of large waves, the agency has said.
Flood risk manager Jonathan Day said: "We are monitoring the situation closely with the Met Office and will issue flood alerts and warnings as required.
"It’s possible we could see some large waves and spray and urge people to take care near coastal paths and promenades and not to drive through flood water."
People can keep up-to-date with the latest situation on the GOV.UK website or follow @EnvAgency and #floodaware on Twitter.