UK Universities have taught homeopathy
While some universities have since moved away from teaching Homeopathy and other pseudo-sciences, David Colquhoun's Improbable Science Blog documented a few examples in the UK around 2008.
This story was picked up by The Times.
Compiled by trawling the Universities and Colleges Admissions Service and university websites, they conclude that 43 institutions offer a total of 155 "unscientific" courses in areas including homoeopathy, traditional Chinese medicine, acupuncture, Ayurvedic medicine, aromatherapy, Naad yoga (healing through music) and general complementary medicine.
It was also picked up by Nature: Article, Special Report
For example: Thames Valley University:
Thames Valley University is one of those shameful institutions that offer Bachelor of Science degrees in homeopathy. They don’t stop there though. They’ll teach you several other forms of make-believe medicine. Among these is “nutritional medicine”. This is taught at the Plaskett Nutritional Medicine College which is now part of Thames Valley University.
Are they reputable?
The question as to whether they are reputable is troublesome, partly because that isn't a well-defined idea.
For example, the Thames Valley University, mentioned above, (and now part of the University of West London) was a proper accredited public university, not some backyard operation. It now (in its modern form) has over 47,000 students. Is that sufficient to be considered "reputable"?
Another aspect is that a university may have many departments which have varying reputations.
We can use the Complete University Guide league tables as a proxy for reputation.
The University of Westminster (mentioned in the articles, about 24,000 students) is ranked in the "leagues tables" as the 4th best university in the UK in the area of Complementary Medicine. So, it has a good reputation for complementary medicine!
Overall, however, it rates 96th overall (out of 123).
The University of Lincoln offers a BSc in Herbal Medicine and is overall ranked 55th of 123, which I think could fairly be described as reputable.