Travel disruption also continues for motorists, with a number of roads closed due to the flooding.
Meanwhile, Great Western Railway said services between London Paddington and Swansea via Bristol Parkway were cancelled due to heavy flooding.
Customers are being asked to complete their journeys before 19:00 GMT this evening because “water levels are so high,” said Paul Gentleman, head of external communications at GWR.
“There is the danger that we could see more line closures and some cancellations, we’re not really going to know until we get that rain appearing this evening,” he told BBC Radio Wiltshire.
A number of flood warnings are in place, external, as watercourses continue to respond to the amount of water running off into them.
“Overnight, the number of flood warnings has actually increased in Wiltshire from 19 to 21,” said Adrian Hampton, head of highways operations at Wiltshire Council.
“So whilst we are seeing an improving picture across the county, we still have a number of flooded areas particularly in the north,” he said.