The water company has been working to fix the burst pipe, which is in a wooded area north of Hastings, throughout Tuesday and will continue to do so overnight.
People are being urged not to stockpile water as “this will make the situation worse”.
“To help keep customers in supply, we also have a fleet of tankers ready to inject water directly into the network if required,” the spokesperson said.
The water company says it will open two “big” bottled water stations on Wednesday as a precaution “in readiness for any issues”, and says it has informed stakeholders, including Dollimore.
The MP said: “My immediate priority is protecting residents, particularly the most vulnerable, and supporting local businesses at this critical time.
“I’ve pressed Southern Water to act fast to open as many water stations as possible, deliver directly to those on the priority services list, and provide extra water to pubs, restaurants and hotels.
“I will be holding Southern Water to account and asking the questions that need to be asked, but right now my focus is on ensuring everyone has access to the water they need and limiting the impact of this.”