Paramedics were called to their home which is barely eight miles from where former Russian spy Sergei Skripal and his daughter Yulia were attacked with a nerve agent in March, which Britain holds Russia responsible for.
The man and woman, both in their 40s, are in critical condition, Wiltshire Police said.
British news agencies have named the two people as Charlie Rowley, 45, and Dawn Sturgess, 44.
British counter-terrorism officers have joined the investigation into how two critically ill people came to be exposed to an "unknown substance" in a town in southern England.
Britain accuses Russian Federation of poisoning the Skripals with a Novichok nerve agent, a group of chemical weapons developed by the Soviet Union during the Cold War.
"We're satisfied that if anyone was exposed to that level of nerve agent by now they would be showing symptoms", he said.
They were initially believed to have fallen ill after using crack cocaine or heroin from a contaminated batch, but are now "receiving treatment for suspected exposure to an unknown substance", Wiltshire Police said.
The Kremlin said on Thursday (Jul 5) it had offered Britain its assistance in investigating a nerve agent attack on a Russian former spy and his daughter in Salisbury in March long ago, but had been rebuffed.
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Public Health England - UK's national health body - has said that there is no significant health risk to the public, but counter-terrorism police have now taken over the investigation.
It remains unclear how the two people came into contact with the nerve agent or whether they had been specifically targeted.
The investigation and cleanup effort after the Skripal attack took over two months, with businesses across Salisbury finding themselves behind police lines forced to remain closed for extended periods.
Church secretary Roy Collins said: "Last weekend we held a community fundraiser and we understand this may well be the last event this couple went to in public".
Senior British officials held an emergency meeting in London to discuss the incident, and will meet later again on Wednesday, a Downing Street spokeswoman said.
While the United Kingdom and the United States blamed Russian Federation for the attack on the Skripals, authorities have not assigned blame for the latest incident and it's unclear if the cases are related.
She issued "highly precautionary" advice to those concerned and said: "As before, my advice is to wash your clothes and wipe down any personal items, shoes and bags, with cleansing or baby wipes before disposing of them in the usual way". Doctors say they don't know the long-term prognosis.
"I do want to reassure the public, however, that there is no evidence that either the man or woman recently visited any of the sites that were decontaminated following the attempted murders of Sergei and Yulia Skripal".