Scotland Yard said in a statement: “As you would expect, given the recent events in Salisbury, officers from the counter terrorism network are working jointly with colleagues from Wiltshire Police regarding the incident in Amesbury.
“As Wiltshire Police have stated, they are keeping an open mind as to the circumstances surrounding the incident and will update the public as soon and as regularly as possible.”
Police declared a major incident on Tuesday after the pair were found unconscious in a house in Muggleton Road on Saturday night.
They are both being treated at Salisbury District Hospital.
The town of Amesbury is roughly eight miles from the city of Salisbury, where former Russian spy Sergei Skripal and his daughter Yulia were targeted with the nerve agent novichok in March.
Police initially believed the Amesbury pair, who have not been named, fell ill after using heroin or crack cocaine from a contaminated batch of drugs.
But further tests are now taking place to establish the substance, with police said to be “keeping an open mind” as to the circumstances around the case.
Officers were seen outside a Boots branch in Amesbury.
Boots UK said: “We can confirm that one of our stores in Amesbury has closed this morning as a precautionary measure at the request of the police as part of their standard investigation protocol.
“We would like to apologise for any inconvenience this may cause customers and patients, and our team are available to direct patients towards our Salisbury Street store where they will be able to access their prescription medicines.”
It is believed one of the last places the couple were seen in public was a family fun day at Amesbury Baptist Church on Saturday afternoon.
Roy Collins, church secretary, said: “Last weekend we held a community fundraiser and we understand this may well be the last event this couple went to in public.”
He said he woke to find the church cordoned off by police at 6am on Wednesday.
“We are all quite puzzled and shocked – naturally the connection with Salisbury and recent events there mean there is a heightened public interest,” he added.
By Crimson Tazvinzwa