A man in his 30s has been arrested on suspicion of murder and attempted murder.
He was taken to hospital on Thursday but is now in police custody, a police spokesperson said.
Police said that the victim and suspect were known to each other and they believed there to be no wider risk to the community.
An investigation, led by the Surrey and Sussex Police Major Crime Team, is under way and inquiries remain ongoing.
Det Ch Insp Kimball Edey said: “This investigation is in its early stages and a team of specialist officers are working around the clock to gather as much information as possible.
“Our thoughts are with the family and friends of the victims at this unbelievably difficult time.”
The force added that anyone with information should contact them or the charity Crimestoppers.
