Up till now, 11 men have put themselves forward for the pioneering project, which has been dubbed "chemical castration."
Those receiving the treatment include prison inmates and offenders who have been released from custody and are living in the community, the Telegraph reported.
The volunteers are being given Prozac, which lowers libido, or other categories of drugs known as anti-androgens.
The current project, which is being overseen by Professor Don Grubin, a forensic psychiatrist at Newcastle University's Institute of Neuroscience, could be the first step towards wider use of the technique.
However, experts have warned that it could prove impractical to impose the medication on sex offenders in a compulsory programme.
Prof Grubin said: "I am suggesting that consideration should be given to a formal national clinic. We are in the early stages of that and have had preliminary discussions with ministers about it.
"I certainly think it would be a benefit. A national clinic would work on prescribing and monitoring protocols and allow psychiatrists to gain a second opinion from me."
Professor David Wilson, a criminologist from Birmingham City University, warned that chemical castration should not be regarded as the solution to all types of sex offending.
"I would want to see this very carefully monitored in terms of whether it reduces the number of children who are attacked by predatory pedophiles," said the academic, who has worked with two British sex offenders who took part in similar schemes after being convicted overseas.
"Chemical castration is not a cure-all and it will not simply magic the problem of pedophiles away. It can deal with the physical part of the libido but not the psychological phenomenon. It is only part of the arsenal that should be used against these predatory offenders," the expert said.