And the researchers stress their work is still at an early stage.
Alemtuzumab - a type of drug known as a monoclonal antibody - was created at Cambridge in the late 1970s, and has long been used to treat leukaemia by killing off the cancerous white cells of the immune system.
The latest three-year study, of 334 patients with relapsing-remitting MS which had yet to be treated, found that the drug cut the number of attacks of disease by 74% more than the reduction achieved by conventional interferon-beta therapy.
Alemtuzumab also reduced the risk of sustained accumulation of disability by 71% compared to beta-interferon.
People on the trial who received the drug also recovered some function that had been thought to be permanently lost, and as a result were less disabled after three years than at the beginning of the study.
Tony Johnstone, a professional golfer, who was diagnosed with MS four years ago, on his treatment
In contrast, people given beta-interferon showed signs of progressively worsening disability.
This was confirmed by brain scans in which alemtuzumab patients showed signs that their brains had actually increased in size, while the beta-interferon patients' brains shrank over time.
The researchers said the findings suggested that alemtuzumab may allow damaged brain tissue to repair itself.
However, they stress that more work is needed to confirm the effects, before the drug can be considered for widespread NHS use.
Lead researcher Professor Alastair Compston said: "Alemtuzumab is the most promising experimental drug for the treatment of multiple sclerosis, and we are hopeful that the phase three trials will confirm that it can both stabilise and allow some recovery of what had previously been assumed to be irreversible disabilities."
MS is caused by a fault in the body's immune system which leads it to attack nerve fibres and their protective insulation, the myelin sheath.
This news will rightly bring hope to people living with the condition day in, day out
This damage prevents the nerves from 'firing' properly, and then leads to their destruction, resulting in physical and intellectual disabilities.
Alemtuzumab works by destroying a type of white blood cell called a lymphocyte, which, in MS, plays a key role in causing the damage associated with the disease.
Effectively, this shuts down the immune system, allowing it to re-boot without the original fault.
Dr Alasdair Coles, who also worked on the study, said: "The ability of an MS drug to promote brain repair is unprecedented.
"We are witnessing a drug which, if given early enough, might effectively stop the advancement of the disease and also restore lost function by promoting repair of the damaged brain tissue."
During the trial, 20% of patients treated with alemtuzumab developed either an under-active or over-active thyroid gland.
A small number developed a low platelet count, rendering them vulnerable to bleeding, and in one case this led to a fatality. However, the researchers stress this complication can be easily treated if recognised early.
Lee Dunster, head of research at the MS Society, said: "This is the first drug that has shown the potential to halt and even reverse the debilitating effects of MS and this news will rightly bring hope to people living with the condition day in, day out.
"More work is needed to prove the drug's long-term effectiveness and we are very much looking forward to the results of the next stage of this important research."
Professor Paul Matthews, of Imperial College, London, described the trial as "compelling".
However, he said: "Alemtuzumab was associated with severe adverse events in a small proportion of the patients, suggesting that it would be unsuitable for any patient except those with very aggressive forms of the disease."
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