A major incident was declared by Wiltshire Police last night, three days after the couple, both in their 40s, were found unconscious at a flat in Muggleton Road, Amesbury.
They remain in a critical condition in Salisbury District Hospital, where earlier this year former Russian spy Sergei Skripal, 66, and his 33-year-old daughter, Yulia, were treated after being poisoned by military nerve agent novichok at their home in the city.
Wiltshire Police said it was "not yet clear if a crime has been committed" in Amesbury but have cordoned off several areas believed to have been visited by the man and woman in the hours before their collapse.
They include the the property in Muggleton Road and the area around the Baptist Centre in Amesbury, as well as Queen Elizabeth Gardens and the Town Path close to the Old Mill Pub in Salisbury, eight miles away.
The couple had been to a hog roast and family fun day for Amesbury Baptist Church on Raleigh Crescent Green which was attended by around 200 people. A video posted on the church's Facebook page showed people enjoying bouncy castles, games and food stalls.
Church secretary Roy Collins said: "We understand this may well be the last event this couple went to in public. They are not church members or regulars.
"Nobody else has suffered any ill-effects. There have been no reports of any other incidents.
"It was a beautiful, sunny day and it was a glorious event, there was nothing going on that was nefarious.
"This is a real surprise and shock to us - we do continue to keep the couple in our prayers.
"We are all quite puzzled and shocked - naturally the connection with Salisbury and recent events there mean there is a heightened public interest."
Police said it was initially believed the man and woman had fallen ill from using contaminated crack cocaine or heroin.
Neighbours saw police, fire engines and people in "green suits" arrive at the flat at around 7pm on Saturday. Residents were told to stay inside their home until about 10pm and their gas and electricity was turned off.
"We wanted to know what happened and with the Russian attack happening not long ago, and we just assumed the worst," said college student Chloe Edwards.
A decontamination shower was driven 77 miles to the scene from Swindon over fears that a batch of drugs was contaminated by a rogue substance, according to the Dorset and Wiltshire Fire and Rescue Service.
"It is a standard Haz-mat (hazardous materials) response," said a spokesperson. "We were called in to support the ambulance service as it was feared people could be contaminated."
Wiltshire Police said further testing was ongoing to establish the substance that led to the couple becoming ill.
"We are keeping an open mind as to the circumstances surrounding this incident," the force said in a statement.
"At this stage it is not yet clear if a crime has been committed. A police investigation has been established. In addition, a full multi-agency response has been co-ordinated.
"A number of scenes, believed to be the areas the individuals frequented in the period before they fell ill, will be cordoned off overnight in and around the Amesbury and Salisbury area as a precautionary measure."
Public Health England said in a statement (PHE) advised that it did not believe there to be a "significant health risk" to the wider public.
"The current advice, based upon the number of casualties affected, is that it is not believed that there is a significant health risk to the wider public," said a spokesman. "This will be continually assessed as further information becomes known."
Angus Macpherson, police and crime commissioner for Wiltshire, said there was no reason to think it was "in any way connected to the Skripal case at this moment."
He told BBC Wiltshire: "I haven't seen anything in this incident yet that I would consider to be an overreaction, it all seems fairly textbook."
Last month Yulia Skirpal said she felt lucky to have survived the nerve agent attack which left her and her father fighting for their lives.
They are now living under police protection at a secret location following their release from hospital last month.
The British government has said it is “beyond reasonable doubt” that Russia carried about the attack, which left nearly 40 people in Salisbury needing treatment for exposure to the nerve agent.
Both Salisbury and Amesbury are a few miles away from the government's Defence Science and Technology Laboratory (DSTL) at Porton Down, which was at the centre of the response to the Skripal incident.
Asked about the latest incident in Amesbury, a government spokesman said: "Ministers are being kept up to date."
Additional reporting by Press Association
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