Having been turned down by "classic funders" he is now campaigning to raise the £25,000 needed to carry out analysis of the brain scanning data from the science crowdfunding site Walacea.com.
He compared current attitudes to studying recreational drugs with the Catholic church's clampdown on pioneering Italian astronomer Galileo Galilei in the 17th century.
"The only comparable example is when the Catholic church banned the telescope in 1616," said Nutt, who is based at Imperial College London.
"We've banned research on psychedelic drugs and other drugs like cannabis for 50 years. Truly in terms of the amount of wasted opportunity, it's way greater than the banning of the telescope. This is a truly appalling level of censorship."
The LSD study involved giving the volunteers injections of a 75 microgram dose of LSD before probing the activity of their brains.
Two kinds of scans were used, functional magnetic resonance imaging (fMRI) and magnetoencephalography (Meg) which measures small magnetic fields generated in the brain.
None of the participants reported having a bad experience but three described some anxiety and temporary paranoia.
Dr Robin Carhart-Harris, also from the Imperial College team, said the dose of LSD given to the volunteers was a "tiny speck".
"The effects are quite profound. It would be described as a moderate dose but a moderate dose of LSD can still produce a profound state of consciousness," he said.
"I wouldn't say that it's a dangerous experiment but I would say that LSD has potential negative effects. Probably the crucial one is a bad trip. It's not uncommon for people to have anxiety during a psychedelic drug experience ... the experience can be nightmarish at times.
"What's especially intriguing ... is that people can have a very challenging experience yet afterwards they seem to be somehow psychologically refreshed by the experience. That's how they describe it."
He said there had been no evidence of psychedelic drugs such as LSD triggering psychosis in research studies, although there were anecdotal reports of this occurring through recreational use.
Nutt said LSD was widely studied in the 1950s and 1960s and shown to be therapeutically useful in treating "many conditions", in particular alcoholism.
Since it was made illegal in 1967 it had only been the subject of one clinical study in Switzerland and two neuroscience studies.
- PAA