The healthy volunteers were testing an anti-inflammatory drug at a research unit based at Northwick Park Hospital when they suffered a reaction.
Relatives are with the patients, who suffered multiple organ failure. Two men are said to be critically ill.
An investigation has begun at the unit, run by Parexel, which said it followed recommended guidelines in its trial.
The men were being paid to take part in the early stages of a trial for the drug to treat conditions such as rheumatoid arthritis and leukaemia until they were taken ill on Monday within hours of taking it.
Eight volunteers were involved, but two were given a placebo at the unit which is on Northwick Park Hospital's grounds but is run independently.
TeGenero, which manufactures the drug, apologised to the sick men's families and said the medicine had shown no signs of problems in earlier tests.
The company's chief scientific officer, Thomas Hanke, said he and his colleagues were "devastated" by what had happened.
He said TGN1412 had been tested extensively in laboratories and on rabbits and monkeys, with no adverse effects and no drug-related deaths.
It was the first time the drug, designed to treat conditions such as rheumatoid arthritis, leukaemia and multiple sclerosis, had been tested on humans.
Scotland Yard said officers were talking to the MHRA and doctors.
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North West London Hospitals NHS Trust
Parexel